Like much of black Africa, Nigeria is counting on the Carter administration to make sweeping changes that will increase pressure on white-dominated southern Africa. This faith in President-elect Jimmy Carter is in sharp contrast to the bitterness toward out-going Secretary of State Henry A. Kissinger felt by the United States' second largest source of foreign crude oil.

These great expectations are so emotional, however, that they run the serious danger of foundering unless the new administration's pace of change far outruns the normal evolution of State Department policy.

The hope invested in the untried Carter administration is the opposite of the open hostility that Nigeria's military leadership reserved for Kissinger's African policies.

For the Carter administration, improved diplomatic relations with Nigeria are linked with American self-interest. In recent years, Nigeria, the world's sixth largest oil producer, has become one of the largest foreign sources of crude oil for the United States.

Nearly 50 per cent of Nigeria's 2 million-barrels-a-day production of prized low-sulphur crude is sold to the United States.

U.S.-Nigerian relations deteriorated steadily in 1975 and early 1976. They reached a paroxysm in early spring last year when the xenophobic military junta allowed the United States - and the former colonial power, Britain - to be blamed for an unsuccessful coup attempt in which the chief of State, Lt. Gen. Murtala Mohammed, was killed.

The Lagos government snubbed Kissinger's request to visit Nigeria during this May swing through Africa, which nonetheless provoked hope - and skepticism - after his Lusaka speech pledging American support for black-majority rule in southern Africa.

Over the months Kissinger's shuttle diplomacy won grudging respect, but Nigerian officials never hid their preference for Carter.

They tend to attach perhaps more importance than is deserved to the practical effect on foreign policy of black Americans votes in helping Carter win election. Similary, they prefer to see in Rep. Andrew Young's nomination as ambassador to the United Nations his elevation to Cabinet status. They overlook the fact that U.N. policy is made in the State Department and that foreign policy tends to evolve slowly.

Moreover, the Nigerians have idealized the Kennedy administration's African policy and drawn a parallel between that aura of good feelings in the early 60s and the one they hope the Carter administration will usher in.

In the more immediate past Kissinger tended to act as if Nigeria's economic importance to the United States could be ignored - a reading that the Lagos government seemed to accept if only in terms of its reluctance to take economic reprisal against American interests here no matter how infuriated Nigerians were by U.S. foreign policy.

American dependency on Nigerian oil is known to have South African contingency planners worried lest U.S. concern over unfettered access to Nigerian oil be transformed into policy decisions inimicable to Pretoria. Some time late this year, or in early 1978, Nigeria's gross national product is expected to overtake South Africa's as the largest in subSaharan Africa.

Nigerian government officials have made it plain that they would like the United States to pressure American companies to withdraw their massive investments in South Africa.

In the past, Nigeria has criticized American policy - especially in Angola, where Kissinger was seen as more interested in standing up to the Soviets than in promoting the end of white rule.