It was my first introduction to ''Connemara time.'' We were returning from the island of Inishturk on the northwest coast of Ireland's ''wild, wild, west.'' I had gone out to the island aboard a fishing trawler, but was invited to sail back with Jamie Young and two other members of our party, plus Jamie's yellow dog, named Finn Mac Cool after a local legendary giant.

It would be hard to imagine a more idyllic cruise, the wooden gaff-rigged sloop gliding gently toward shore before the wind, the setting sun gleaming on the water and glistening off tops of mountains and cliffs. Yet the wind was pushing us all too gently, and my friends and I were becoming anxious about our dinner reservations.

Jamie asked us when we were due.

''7:30,'' we said, looking despairingly at our watches.

''Oh, well then, don't worry,'' he replied, settling back against the gunwale. ''They won't be expecting you till nine.''

In Connemara, time doesn't exactly stand still, it just moves very, very slowly. Long summer days end in hours of lingering twilight, and life is paced to the languid rhythms of the sea.

This is a Gaeltacht area, where Irish is still a spoken language and traditional music and crafts have been preserved. Yet a common sight is a new boxlike white house near an abandoned stone cottage.

For the traveler, Connemara is a place where there's everything to do, but you don't have to do anything. You can fish, sail, ride, golf, hike, sight-see, shop for woolens and tweeds - or simply sit on a secluded beach, watching the mist blow off the mountains.

Although long popular with anglers, skin divers, and the more adventurous tourists, the region is also far off the usual tour-bus routes, so you'll find few new hotels and restaurants here. Instead, the fine hotels are mostly former country homes, combining the pace of a by-gone age with 20th-century comfort.

Distances are short, so sightseeing can be leisurely, with plenty of time for taking pictures. You can make a circle tour by car in a day, even though the roads aren't made for people in a hurry.

Connemara is within an easy day's drive of either Shannon or Dublin airports. Yet turn the bend leaving the village of Oughterard, and you enter another dimension.

The change is sudden. One curve in the road, and fields and farmland are transformed into yellow gorse and alternating strata of rock and turf. Mountains rise straight up in treeless cones 2,000 feet above lakes and sea, their slopes graced with heather in summer, their peaks snow-crowned in winter. Shorelines are jigsaw puzzles of peat bogs and rocky cliffs, secluded inlets and enchanted islands.

This is also a harsh land, rock-strewn and difficult to farm. In fact, it seems - to the visitor's eye at least - that what isn't bogland here is rock. A history of hardship can be read in the roofless stone cottages blending back into the craggy landscape. Early Christian monks sought religious isolation here , and it's to this wild land that the Catholics were pushed by the English under Cromwell in the mid-17th century. Two hundred years later, the population was decimated by the great famine.

But travel north from Recess through the Inagh Valley at dusk and you'll understand what James Joyce calls ''the transcendent, translucent glow of our mild mysterious Irish twilight.'' The valley separates the mountain ranges of the Maumturks and the Twelve Bens. Long narrow lakes wind around the Bens, covering much of the valley floor, mirroring the mountains. Occasional patches of pines climb the mountainsides, part of a national reforestation effort to provide much-needed lumber and paper.

In the bogs below, turf cutting goes on in the spring, as it has for centuries, yielding peat briquettes for sweet-smelling hearth fires. There's even a local power plant that runs on turf.

Scattered flocks of sheep graze by the road. You'll notice patches of pink or blue on their coats. These aren't the latest fashion colors for Aran sweaters; it's the method of branding here.

As the road bends west, the spectacular view of Kylemore Abbey is rather startling after the wildness of the Inagh glen. Now a girls school run by Benedictine nuns, the building was a 19th-century Englishman's version of a castle. Local legend has it that the giants Finn Mac Cool and Cuchulain once tossed a boulder back and forth between the mountains here.

On the Renvyle peninsula is the hotel originally owned by writer Oliver St. John Gogarty, a compatriot of W.B. Yeats and James Joyce. In fact, the character of Buck Mulligan in ''Ulysses'' is a rather unflattering portrait of Gogarty.

Rustic and informal, Renvyle House still has a free-spirited air about it. Owner Hugh Coyle will personally offer you seconds at dinner and will keep you singing Irish ditties till the wee hours. (Stop in Limerick or Galway and pick up the three paperback volumes of ''Folksongs and Ballads Popular in Ireland'' before you come.) If you plan to retire early, be sure to request a room away from the lounge. (A room is $25; dinner, $18.)

Just up the coast is Jamie and Mary Young's Little Killary Adventure Centre, a camp for adults and teenagers in a renovated farmhouse and stable. Activities vary from sailing and windsurfing to - surprisingly enough in this remote setting - computers!

Jamie Young, a single-handed ocean racer, will sail you out to the Island of Inishturk, ''if the day is fair.'' You can also book passage for Inishturk from Renvyle House aboard Armin Muck's 33-foot fishing trawler, Village Girl. Because it operates on Connemara time, the boat doesn't leave at the crack of dawn. Our group had time for a 9:30 horseback ride first.

The waters around Inishturk are rich with sea life - lobster, crayfish, crab, tiny but succulent mussels - and the island population of about 120 is supported by fishing. In the harbor village, there's a post office, a pub, a church, a few homes, and a lone telephone booth up the hill, shades of the film ''Local Hero.''

Delia Concannon, a village resident, will serve you lunch, if you let her know you're coming, either through Armin Muck or the Renvyle House. Mrs. Concannon serves whatever the fishing boats bring in that day. Our $10 lunch was vegetable soup, a huge crayfish with a tangy homemade mayonnaise, beets, cucumbers, and the best brown-bread scones we had in Ireland. You are free to roam the island - just be sure to tie the sheep gates behind you. Climb to the top of the treeless hills, and you can see across miles of islands, sea, and rocks to Croagh Patrick, the mountain where, according to legend, St. Patrick fasted for 40 days and nights before casting the snakes out of Ireland in the 5 th century.

A larger island, Inishbofin, can be reached by mail boat from the village of Cleggan.

From Renvyle, it's only a few miles to the new National Park at Letterfrack. The park preserves a variety of Connemara habitats: mountains, heaths, bogs, grasslands, woodland, and seashore. Also in Letterfrack is Connemara Handcrafts, a shop that bills itself as ''possibly the most interesting craft shop in the west.'' It very possibly is. You'll find everything from glassware, jewelry, and Aran sweaters to musical instruments and songbooks.

Clifden, the largest town in Connemara, is a center for sea fishing. The popular Connemara pony show is held here at the end of summer, and there's a 10 -mile scenic Sky Road that is worth driving. If you haven't purchased your Aran sweater by this time, stop in at Millar's Tweeds.

Just south of Clifden off the Ballyconneely road is a memorial to the first trans-Atlantic nonstop flight, by Alcock and Brown, who landed here in 1919.

At the head of Cashel Bay on the southern coast are two lovely hotels. Zetland Hotel and Fisheries has the graciousness of a 19th-century sporting lodge, but it has been newly renovated to give it an open, contemporary style. Seafood, of course, is a specialty in the dining room, but don't overlook the beef, which is from a local ranch and is superb. (Room, $38; dinner, $20.)

Nearby Cashel House is a gem of Victorian elegance in a 50-acre setting of flowering gardens. The hotel hosted General de Gaulle and his wife in 1969, and its atmosphere is geared for ''a restful holiday.'' (Room, $30; dinner, $22.)

''A restful holiday'' is something in which this region of Ireland excels. At the end of a Connemara day, as you feast on smoked salmon or sit with your feet up by a turf fire, you might remember the story of the visitor who was trying to explain the Spanish word manana to a Connemara man. The visitor said that it means ''tomorrow,'' and then asked, ''Do you have an equivalent word in Irish?''

The Connemara resident thought awhile, then replied, ''We don't have anything as hasty as that.'' Practical information:

Prices are per person in season, including gratuity, and are based on an exchange rate of $1.34 to the Irish pound. Room rates include breakfast. All hotels listed here are A-rated by the Irish Tourist Board. (It's advisable to choose hotels rated B* or better.)

Guidebooks are available from the tourist board for hotels, restaurants, and bread-and-breakfast accommodations. Check with your travel agent or write: Irish Tourist Board, 290 Fifth Avenue, New York, N.Y. 10036.

Write: Little Killary Adventure Centre, Salruck, Renvyle, County Galway, Ireland.

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