Kuwait has moved to expand its air defenses by increasing its military ties to both the United States and the Soviet Union in recent weeks.

The strategically placed Persian Gulf kingdom has decided to send 150 cadet pilots to the United States for training and has asked Washington to set up a pilot training school here, according to western diplomatic sources who view this as one sign of significant improvement in previously strained U.S.-Kuwaiti relations.

At the same time, half a dozen Soviet military experts have arrived here in connection with the Kuwaiti purchase of Soviet-made SA8 surface-to-air missiles.

While Kuwait already had the Soviet SA6 and SA7 antiaircraft missiles, the arrival of these experts marked a departure from past Kuwaiti policy of not allowing Soviet military personnel to base themselves here for training purposes.

Reports of the initial Kuwaiti- Soviet agreement had raised concern in Washington that it might compromise the security of equipment the United States was offering to sell Kuwait, particularly that needed to relay information from Saudi-based U.S. Airborne Warning and Control System (AWACS) aircraft directly to Kuwait.

Despite these key developments involving the two superpowers, the Kuwaitis also have kept both Washington and Moscow at arm's length on other major anticipated deals.

Kuwait still has not acted on a $82 million emergency air defense package offered by Washington last June when escalating Iranian air attacks on oil tankers in the Persian Gulf, including several Kuwaiti ones, raised fears here of a possible larger Iranian attack on a vital oil installation.

Nor has Kuwait signed a major arms deal with the Soviet Union, according to these sources, despite press reports last July that it had reached agreement in principle with Moscow on a $327 million purchase. Although the Kuwait News Agency announced the formal signing of a Soviet military aid agreement in August, these sources say this was only a $30 million contract to purchase antiaircraft missiles for Iraq and to finalize an earlier deal for the purchase of the SA8 antiaircraft missiles.

With the Persian Gulf "tanker war" now abated and with France and Saudi Arabia helping Kuwait boost its meager air defenses, the government here seems to be taking a more relaxed, more long-term view of its air defense needs.

Some western diplomatic sources believe Kuwait is still hoping for a change in policy in Washington that would allow it to obtain F16 jet fighters, heretofore banned to all the small Arab emirates and sheikdoms of the Persian Gulf.

This could explain its decision to send more Kuwaitis to the United States for pilot training, according to some western analysts here. Thirty-two of the 150 cadets already have left.

U.S. officials in Washington said, however, that there has been no change in the U.S. policy barring sale of the F16s to the Persian Gulf states and that no decision is pending on any such change.

In any case, Kuwait seems to be making a conscious effort to improve its relations with Washington. The usual anti-American flavor of the Palestinian-influenced press here has been toned way down, and the new U.S. ambassador, Anthony Quainton, reportedly has received royal treatment since his arrival in September.

The midsummer reports of a big Soviet arms deal, coinciding with a trip to Moscow by Kuwaiti Defense Minister Salem Sabah, were "a sort of bluff for Washington," said a Western European diplomat.

The primary purpose of the "bluff," according to one well-placed Western European diplomat, was to provoke the United States into offering Kuwait more sophisticated weapons, especially the F16 and possibly the shoulder-held Stinger antiaircraft missile.

Kuwait needs to replace its aging, American-built A4 Skyhawk jets and would like to obtain the far more sophisticated F16 as a substitute, the diplomat said.

The Kuwaitis never formally have asked to purchase the F16. In June, when they informally asked about the Stinger missile, they were turned down because of congressional opposition to the sale. This experience has made them reluctant to ask for anything that might again be rejected or hotly debated in Congress to their embarrassment.

While Kuwait has made no formal decision on the proposed $82 million air defense package offered by Washington, western diplomatic sources said they believe it has decided not to accept, partly because the perceived crisis of last June has passed and partly because of complications with Saudi Arabia over the sharing of information provided by the Saudi-based AWACS planes.

The U.S. offer included the sharing of AWACS information on an instantaneous basis through a direct hookup with the Saudi command center. According to some reports here, the Saudis were not anxious to share all the AWACS data with Kuwait.

However, Saudi Arabia has lent Kuwait a radar station through which it obtains partial information from the AWACS planes.

In addition, France, which is providing Kuwait with an overall command and control system including six radars by 1986, has rushed two less sophisticated radars to Kuwait to fill the gap.

The French also have sold Kuwait an additional 13 Mirage F1 fighters as part of the $650 million worth of arms they sold here last year. The first of the 13 is due to arrive here in December, with one to come every subsequent month.