Bonn — Just beyond the concrete-and-glass buildings in Bonn's government quarter where the major parties have their headquarters stands a little bungalow with a sunflower sign protruding from a garden of weeds.
Until recently, establishment politicians could allow themselves a quiet sneer as they drove past the humble home of the ecologist ''Green'' Party. But these days, the very sight is enough to send shivers down the spine of any West German politician.
''What shall we do about the Greens?'' is the question plaguing party strategists now that the federal capital has emptied for the annual summer recess.
The dilemma is most acute for Chancellor Helmut Schmidt's Social Democrats (SPD), whose voters have been defecting in droves to the loosely knit coalition of leftists, environmentalists, and pacifists. But it is hardly less pressing for his Bonn coalition partners, the liberal Free Democrats (FDP). They have just been overtaken for the first time in a national public opinion poll by the Greens.
If a general election were held tomorrow, the opponents of atomic power and nuclear missiles would march into parliament as West Germany's third political force with a handsome 7.7 percent of the vote, the sober Allensbach Opinion Research Institute found.
The prediction is already a reality in several state parliaments. Greens or alternative groupings are represented in Hamburg, Hesse, Lower Saxony, Baden-Wurttemberg, Bremen, and West Berlin.
The Greens, who proclaim themselves to be the ''anti-party'' and boast they are the only party not financed by donations from big business, are the country's fastest-growing political force. Their youth audience extends far beyond their membership of 25,000.
They have surged ahead on a new wave of disillusionment at the bland consensus politics that have led West Germany slowly but surely into economic austerity, environmental pollution, and military rearmament.
Success has come fast for the infant movement, founded as a national party only in 1978. Now its leaders are wondering whether it should cooperate with the major parties in an attempt to achieve some of its political aims.
In Hamburg, where a Green-Alternative List with nine deputies holds the balance of power in the city-state's parliament, the Social Democrats have just begun talks for the first time with the newcomers to see if there is scope for limited cooperation.
In return for supporting a minority SPD government, the Greens are demanding the phasing-out of all Hamburg's nuclear power plants, an end to plans to enlarge the city's port facilities, an immediate program to clean up the Elbe River, and more public spending on education and housing.
Spawned in the 1970s by the campaigns against nuclear power and other big technological projects, such as the disputed plan to extend Frankfurt airport, the Greens have made their biggest gains in the last 18 months as a powerful antinuclear peace movement has emerged in West Germany.
As East-West relations soured and military budgets soared, the Greens were the only national party to oppose NATO plans to put new US medium-range nuclear missiles in Western Europe next year unless Moscow agrees to scrap its missiles. It requires no prophetic gift to predict that the ecologists will gain still more support as the deadline for deploying the Western missiles draws nearer.
The challenge posed by the Greens is almost as much a question of style as of policy. The party believes in involving citizens more directly in government, is deeply suspicious of professional politicians, and is not always prepared to accept the rule of law.
This has led right-wing politicians to draw parallels with the early days of the Nazi movement - a comparison the Greens and most of the West German left reject with indignation.
Petra Kelly, one of the party's three national chairmen and the nearest thing the Greens have to a national leader, is worried that the movement could grow too fast, before it has built a coherent strategy.
''I'm not sure we are ready for all the responsibility which success is bringing us,'' she admitted recently.
Electoral success contains several dangers for the Greens. If they decide to compromise with Social Democrats to make progress on some of their demands, they run the risk of forfeiting many of their idealistic young supporters. If they remain uncompromising, they could block the political system without achieving anything.