Nothing better illustrates the cross-purposes at work in the Reagan administration's grand design for Mideast security than the first fruits, so to say, of its splendid victory on the AWACS sale to Saudi Arabia.

The first fruits are to be found in a series of Israeli responses so sour in tone and distended in content as to put at risk the successful achievement of either of the two purposes the administration is trying to achieve. One purpose is some sort of military counter-weight to Soviet/communist incursion in the area. This means creating a rich mixture of American (and Western) air, ground and naval presence in and near the Persian Gulf.

The second purpose, inextricably connected with the first, is to advance the "peace process," building n the Camp David accords with a view to defusing the explosive Palestinian issue and ultimately resolving it. For now, this means not just completing that part of Camp David having to do with an Israeli-Egyptian peace treaty, but proceeding with the plan for an interim "autonomy" arrangement on the West Bank and Gaza.

The AWACS sale was supposed to serve both purposes. Given the Saudis' reluctance, for their own political reasons, to grant the United States ground bases and the right to overfly Saudi air space with its own AWACS, the transfer of title of these sophisticated airborne warning and control systems to Saudi Arabia was considered the next best thing.

The Saudi AWACS would be compatible with the F15 fighter-bombers the Americans could rush to the scene in a crisis. They would provide a pretext for "overbuilding" support facilities in Saudi Arabia and a justification for "pre-positioning" supplies, spare parts and all the rest.

But to make palatable to the Senate what seemed to many an unreasonable Saudi resistance to a full-fledged strategic relationship, it became necessary to present the Saudis as substantial contributors to past peace-keeping efforts, flexible about future initiatives. The most solid evidence was a bright glimmer of conciliation in an eight-point Saudi Arabian "set of principles" for peace--a glimmer that had somehow escaped the administration's notice when the Saudi "principles" were first put forth by Crown Prince Fahd early last August.

Now, there is something to all this. The Fahd plan does hint at recognition of Israel's right to exist. The prospect of a more forthcoming Saudi contribution to the "peace process" is not to be lightly dismissed. But the effect of the administration's focus on the Fahd plan was to give what was only an opening bargaining position the status of a credible substitute for the flagging Camp David approach--the more so since it is simultaneously receiving a warm embrace from European "peace initiators," led by the irrepressible British.

At an Arab League summit this month, a major effort will be made by the so-called moderates to make the Fahd plan the pan-Arab answer to Camp David--and why not? It would create an independent Palestinian state, with East Jerusalem as its capital, require the dismantling of all Israeli settlements on the West Bank and roll Israeli occupation forces back behind the pre-1967 War lines.

Everything about the Fahd plan, and about its emerging prominence in the peace-making process, then, could be counted on to contribute mightily--even justifiably--to Israel's understandable sense of insecurity and encirclement. But that is not the same thing as saying that everything about the massive Israeli counteroffensive, on just about every front, is as likely to contribute in the long run to Israel's security.

"Truth squads" have been dispatched by Menachem Begin to Congress and Cabinet offices and across the country to denounce the Saudis, and to warn of massive flows of arms to the Arabs. A team of military experts is here to promote a "strategic cooperation" arrangement with the United States that would include base rights, naval facilities, joint maneuvers.

The Israelis want not more arms, but U.S. credits to finance Israeli research and development to produce their own high-technology weaponry (radar-jamming devices, for example) to counter the sophisticated stuff the Saudis are getting. They want a U.S.-Israeli military connection on a scale that, if agreed to, would almost certainly compromise United States efforts as an Arab-Israeli intermediary, as well as upset the more balanced area-wide "strategic consensus" the Reagan administration is seeking.

Meanwhile, back on the West Bank, a new crackdown is under way against Palestinian terrorism. New settlements are planned. At the same time, the Israelis are scaling down their military presence and encouraging a larger degree of self-rule by Palestinian moderates in a way that could co-opt the Camp David autonomy formula by introducing at least the look of "de facto autonomy." Begin's unspoken, ultimate aim is annexation.

The American grand design, in short, is in danger of cracking apart. Sorting out, and reconciling, its inherent contradictions is going to require a lot more careful handling than was evident in the administration's handling of the AWACS deal.