Argentina begins to resolve its many - and costly - international disputes

President Raul Alfonsin's efforts to tidy up Argentina's many international disputes are beginning to bear fruit. First on his agenda is the ''practically complete'' agreement to end the dispute with Chile over the Beagle Channel.

Next is likely to be the much more difficult and emotional dispute with Britain over the Falkland Islands - a dispute that erupted into a disastrous and costly war for Argentina in 1982. Preliminary talks toward finding a solution to the Falklands issue are already under way.

For the moment, attention is focused on talks with Chile over the Beagle Channel. Barring any unforeseen hitches, spokesmen for the Argentine and Chilean foreign ministries said this week that the Beagle accord could be signed within two weeks. This would prove a happy ending to a bitter dispute that has almost brought the two nations to the point of war several times in the past decade.

Although neither side has disclosed details on the accord, it is reliably understood that each has modified its stand. The dispute centers on the actual course of the Beagle Channel at the tip of South America and on control of three islands, Lennox, Picton, and Nueva.

Argentina apparently has accepted Chilean sovereignty over the islands and an east-west course for the Beagle Channel. The accord is along the lines of the ''binding'' British arbitration award of 1978, which Argentina rejected, and two subsequent papal decisions.

In return, it is understood that Chile will give up some of its claims to the waters on the Atlantic side of Cape Horn, except for 12-mile jurisdiction around the three islands and other Chilean territory in the region. Chile will, moreover, share in some Atlantic resources.

Not all Argentines or Chileans will be happy with the accord. But in Argentina, President Alfonsin apparently has enough clout to get a treaty ending the dispute through the ratification process.

And the Argentine military, which repeatedly put stumbling blocks in the path of a Beagle accord in the late 1970s and early '80s, is now out of power and much discredited. It is unlikely the military could scuttle the accord - although it will serve as a potent support for the deep cuts in military spending that Alfonsin wants.

But the Falklands dispute is different. It is a much more emotional issue for Argentines. And the military particularly worries about talks with Britain.

President Alfonsin is running into plenty of verbal flak in his efforts to resolve the dispute. Anything short of full Argentine control of the islands, which it calls the Malvinas, will be rejected by large segments of the Argentine populace.

From early school days, Argentines are taught, ''Malvinas son nuestras (The Malvinas are ours).''

Alfonsin agrees. But he also says solution of the dispute, with some Argentine compromise, is necessary. He argues that it is draining too much Argentine energy ''that must be directed at more pressing problems,'' as he put it during his presidential campaign last year.

This week Alfonsin said that talks with the British about the Falklands ''are only beginning.''

But the fact that the talks are getting under way shows Alfonsin's determination to get Argentina out of the ''morass of controversy that has haunted our nation domestically and on the international scene,'' he said recently.