ANCHORAGE, JUNE 18 -- Like spendthrift playboys cut off from the family fortune, the people of America's most oil-dependent state have begun to experiment with life as it is lived in the rest of the country -- paying taxes, struggling with deficits, getting behind on the mortgage and looking for work.

After two years of hoping that their favored life styles can survive the long fall of oil prices, Alaskans have begun to lower their sights and accept new taxes, fees and financial difficulties unthinkable five years ago.

Leading the change is a new rough-edged governor, Steve Cowper (D), a Fairbanks lawyer who grew up in North Carolina and Virginia. He has dared to suggest cutting back the flow of oil checks to Alaskans of every walk of life and persuaded a recalcitrant legislature to reduce, at least slightly, some favored state benefits.

"There are a number of programs in this state that are simply not available to anyone else in the country," Cowper said. In an interview, he acknowledged that his stand has created an enormous outcry, but insisted that "persistance usually pays off and people do what is necessary."

Whether the price of oil stays at its new $20-a-barrel level or not, Alaskans already are resigned to an economy that may never return to the boom days of the early 1980s, when oil stood above $35 a barrel. This week the state is celebrating the 10th anniversary of the first flow of oil from Prudhoe Bay on the north slope through the Trans Alaska Pipeline. That flow continues, at reduced prices, and a rich new field may come on line by the year 2000. But, just as in Louisiana, Texas and other states whose fortunes as oil producers have ebbed, everyone is adjusting to worse times.

Several hundred hard-pressed Anchorage residents formed long lines this spring to sign over their annual state permanent fund dividends -- expected to bring each of them about $750 this fall -- to private speculators for $325 in immediate cash. People in line told local reporters of long-overdue mortgage payments on their trailers and related other stories "that just broke your heart," said Cowper spokeswoman Laury Roberts Scandling.

The unemployment rate is up to 11.8 percent, housing prices have slumped 20 to 30 percent, mortgage foreclosures have soared and an economy that once attracted a steady stream of hopeful young workers from the lower 48 states is losing nearly 1,000 jobs a month.

Local governments have begun to consider sales taxes, unheard of in most of the state, and to cut such accustomed luxuries as out-of-state trips for the local high school band and basketball team -- no small item when the border of the nearest state is 450 miles away.

The state government is about to lay off 1,000 more employes, and the legislature has agreed to seek repayment of liberal college loans immediately after graduation and no longer forgive half the loan of anyone who stayed in the state for five years after receiving a degree.

There have been no serious efforts to follow through on Cowper's more radical proposals -- a state income tax or restricting $250-a-month state senior citizen bonuses to the needy. But Cowper, 48, has confidently called the legislature back for a special session July 1 to handle a $317 million deficit. He proposes taking the money from earnings of the $9 billion state permanent fund, the nest egg set up to help the state through the difficult future days when oil no longer flows.

The special session marks the latest battle between Cowper and legislative leaders, particularly Senate President Jan Faiks, over handling the drop in oil revenues. Despite the recent surge in oil prices, the state estimates next year's oil price at about $14 a barrel. The state Senate majority based its revenue projections on $16 a barrel instead and adjourned without dealing with the deficit the official state per-barrel price projected.

Faiks, 41, a Republican businesswoman from Anchorage, has concentrated on budget matters and supports lower state spending, but has resisted calls for tax increases.

"Our future looks very bright," she said. She pointed to new mineral enterprises, such as the Red Dog lead and zinc mine, and the recent plentiful harvest of bottom fish. A predicted drop in production this year as Prudhoe Bay's ancient oil pools begin to dry up has been postponed to 1989. And the proposed opening to wildcatters of a portion of the Artic National Wildlife Refuge could bring another surge of oil revenues in a decade.

George L. Whyel Jr., president of the First National Bank of Fairbanks, said the recession there will be cushioned by the arrival of a brigade of the new 6th Light Infantry Division, bringing 7,000 soldiers and dependents and $300 million in construction projects.

The sharp drop in the state's construction industry probably would have happened without an oil price decline, University of Alaska economist Scott Goldsmith said, due to "overstimulation of the industry" in the early 1980s.

Cowper, Faiks and other Alaska politicians agree they must diversify the economy through more tourism, fishing, minerals and natural gas. Just what they will do with the oil money, which continues to pay most of the state's $3 billion budget and add to the permanent fund, remains to be seen.

Former governor Jay S. Hammond (R) proposed the annual permanent fund dividend payments to every state resident in order to protect the fund from raids by greedy politicians. If voters had a regular stake in the interest from the fund, he argued, they would fight any attempt to drain the principal.

Cowper has not proposed ending the annual dividend, but has suggested voters be asked to choose between that or new taxes. He thinks such handouts are luxuries in a state trying to balance its books. "The fund has a faithful and attentive constituency," he said, "that has no relationship to the dividends."