After the crises

President Reagan now begins the second week of the most serious testing of his foreign policy leadership. The most acute phases of the Lebanon and Grenada crises lie behind him. Now comes the equally difficult test of devising post-crisis policies for the two regions.

So far, has President Reagan come out behind or ahead? What should he next do?

Of the two crises, Grenada offers the President a quicker exit, if not a better chance of ''success.'' Lebanon, where reconciliation talks were scheduled to begin today, looks like a longer, tougher slog.

First Grenada: On the plus side, Mr. Reagan's conservative friends at home feel better after the Grenada invasion. They think the Cubans, Soviets, Iranians , North Koreans, Nicaraguans, or any other adversaries will think twice before they challenge the hitherto reluctant United States military giant and make mischief in other countries. Mr. Reagan's address to the nation last Thursday, focusing on ''a Soviet-Cuban colony being readied as a major military bastion'' on the island, will also sound convincing to many Americans as justification for the administration's invasion.

The public's opinion of the Soviet Union is at its lowest point since 1956. Cuba is no more popular. The assertion that US medical students' lives were saved, and the portrayal of the US military in an active, rescue-mission role in Grenada in contrast to its sitting-duck posture in Lebanon, were no doubt welcome to many Americans.

The minuses are as weighty. The invasion prompted a United Nations Security Council condemnation, with France and other allies voting with the Soviet Union and China against the US, and with Britain abstaining. The charges: a grave violation of international law and evidence of renewed Yankee imperialism. The image of tarnished moral superiority for America could be used to justify stronger popular resistance to deploying more NATO missiles in Europe in coming weeks. At home, the invasion started the War Powers Act ticking, many in Congress assert. That means a confrontation between the White House and Congress over Grenada, muted while troops are in action, could break out in full force when the two-month period for sending troops on an invasion without congressional consent is over.

In Lebanon, the chief advance in President Reagan's public statements was his inclusion of Israel's interests in the framework as a justification for continued American involvement in the region. But there was still no acknowledgment of the shifting power balance to Syria's benefit, no naming of a new American envoy, nothing of a practical diplomatic nature to suggest a new policy and framework for peace.

At home, Mr. Reagan has so far been spared demands that the Marines be pulled out of Lebanon. But a domestic time clock is ticking there, too, for the administration to get a new initiative launched. A substitute peacekeeping group made up of neutral forces must be found. President Gemayel must be persuaded to yield more power to the Muslim majority. Syria's greater leverage must be taken into account. And none of this can go forward without approaching the more fundamental sources of tension - chiefly Palestinian rights in the occupied territories and the Golan Heights. It was, after all, the Palestinian stronghold in Lebanon that drew in first the Israelis and then the US Marines to cover the defeated PLO's pullout. The Marines did not go there to halt a Soviet advance.

Events like last week's stir caldrons of tension that produce ever new questions. In Grenada, if the US invaders were surprised to find a budding Cuban-Soviet bastion, how could that have been a motive for invading? Why had US intelligence been so lacking? Were students in greater danger from invasion cross fire than from the Grenadian regime itself? What are the plans for a successor Grenadian government? In Lebanon, why had warnings of car-bomb attacks gone unheeded? Will there be a military investigation?

These are among this week's questions for an already hard-tested White House.