Brussels — The 33-year-old Atlantic Alliance has welcomed Spain as its 16th member, expanding NATO's defense capability but further threatening its already shaky internal cohesion.
The signing Dec. 10 of the protocol of Spain's accession to NATO comes only 24 hours after Greece and Turkey succeeded in bringing a NATO defense ministers' meeting to a standstill with bitter arguments over bilateral questions.
At a time when Greece and Turkey have brought their longstanding quarrels to the NATO forum and when some European countries have questioned the Reagan administration's call for increased NATO defense spending, analysts argue that the Alliance needs more glue. Spain's entry, they believe, will provide it.
It will also provide some generous military advantages.
Spain's position on the extreme Western flank of Europe would offer, in the event of war with the Soviet Union, a rear base for stockpiling materiel. Its strategic setting will offer surveillance posts for Mediterranean and Cape shipping routes - particularly interesting to countries in northern Europe. And Spain boasts 220,000 troops, plus an Air Force and Navy.
But with the military hardware and advantages also come sideshows that could be divisive for the Alliance:
* The Spanish government has said it will not accept nuclear weapons on its soil. As other European countries, especially the Netherlands and Belgium, face growing public protests against NATO plans to deploy new nuclear missiles in their backyard, reluctance by a new NATO member to do so is bad news for military planners.
* There is also a deep undercurrent of nationalism, even neutralism, in Spain. The strong Spanish Socialist Party has said it will wage war against entry into NATO. Greece, whose recently elected Socialist government has emitted loud noises threatening withdrawal from the military wing of NATO, could be led to support its party allies in Spain. This would leave the Spanish government to defend NATO membership against a domestic opposition backed by the government of another NATO country.
* The Soviet Union - not surprisingly - believes that an expansion of the Western Alliance will have an unhealthy effect on the balance of psychological power between East and West. For that reason, some political observers suggest that Spanish entry could sour international relations just at the moment when they need to be sweetened.
* News of Spanish entry is also bound to unleash a wave of protests from the European peace movement, which in the past two months has brought 2 million demonstrators into the streets against the superpower military buildup.
Spain's smooth integration into the NATO command, the US believes, is important for the Atlantic Alliance. Moreover, it will give a needed boost to the revitalization of the Spanish armed forces and to American military interests in the country. One of three American air bases is now in mothballs. Still, more than 10,000 US servicemen are stationed in Spain, and about 50 communication and radar facilties and bombing ranges exist in the country.
NATO analysts say that Spanish entry (full membership status will not come for many months) could seriously test the cohesion of the Alliance, perhaps not as dramatically as Greece and Turkey have, but just as profoundly.
''Yes, it will be a test,'' a longtime NATO observer said.