Two of the more remote places in America - steele County, North Dakota, and Prince of Wales Island, Alaska - were the richest places in the country in 1974 in terms of per capita income, according to U.S. Census Bureau estimates.

Steele County, a grain farming area that boomed with record-high wheat prices, had an average income of $12,124 for each of its 3,550 residents, the Census Bureau said.

Prince of Wales, a rainy wooded island at the Southernmost tip of Alaska, had a per capita income of $8,510, the bureau said, as its logging camps flourished with massive exports to Japan.

The island, off the coast of British Columbia, has a population of 2,641. Residents get their groceries, one of them said, by freighter from Seattle, about 1,200 miles away.

"We don't think of ourselves as an high-income community," said Marvin Yoder, the mayor of Craig, the island's biggest settlement (population 357). "But I guess we're doing quite well now."

Arlingoton County, Va., which had the country's highest per capita income in 1969, as reported by the 1970 census, fell to third place in 1974 with an average of $8,493.

It held on much better, though, than the borough of Manhattan in New York City, which was the second highest income county in 1969 but fell to 56th in the 1974 per capita income tabulation.

Five other Washington suburbs remained high on the per capita income list - Falls Church (8th), Montgomery County (12th), Alexandria (18th), Fairfax City (20) and Fairfax County (25th).

All of them rely heavily on federal government salaries, contracts, and pensions, which continued to grow during th recession of the early 1970s.

On the other hand, three New York City suburbs - Westchester and Nassau counties in New York and Fairfield County in Connecticut - dropped out of the top 10, where they had been in 1969, to 29th, 47th and 49th respectively.

Nine other big cities and suburbs throughout the country also dropped off the list of the 25 richest places.

They were replaced by Midwestern farm countries, prospering, from high prices for their crops, and by places in Alaska, which is booming from construction of a multibillion-dollar oil pipeline.

The 1974 list of the 21 cities and counties with the highest per capita income has 14 farm counties on the Great Plains, including seven in North Dakota, four cities and counties in Alaska, six Washington suburbs, and only one suburb elsewhere in the country, Marin County, just across the Golden Gate Bridge from San Francisco, which ranks 22d.

"1974 was a great year for farm prices," said Daniel Burkhead, the Census Bureau statistician who is in charge of compiling the per capita income figures. "But they haven't held up since then. Farming has its good years and its bad years, you know. The list [of richest counties] will probably look different the next go around."

In Steele County, North Dakota, which is about 75 miles northwest of Fargo, Joseph Knudson, a 69-year-old farmer who serves as a county commissioner, said the price of durum wheat has fallen from its high of $4.85 per bushel in 1974 to about $2.35 per bushel now.

The price rose sharply, he said, after huge U.S. wheat sales to the Russians in the early 1970s.

The prices paid by farmers for fuel and equipment also rose substantially, Knudson said. They remain high, he said, despite the fall in crop prices, putting many farmers in a financial squeeze.

"We don't feel so well off now." Knudson said. but he added: "Farming has changed a lot from what it used to be. The farms are much bigger now and there's a lot more equipment."

Per capita income is computed by adding the income received by all residents of an area, including wages, dividends, pensions, and welfare payments, and dividing the total by the area's population.

The Census Bureau also computes median family incomes, showing the midpoint at which 50 per cent of the families in the area make more and 50 per cent make less. However, the median figures have not been updated since the 1970, census, when Montgomery County, Md., ranked first in the national followed by Fairfax County, Va., and Nassau, N.Y. Arlington County then ranked ninth on the family income list.

Officials explained that Arlington's per capita income is higher than that in Montgomery and Fairfax because its average family size is much smaller.

According to the 1974 figures, Washington had a per capita income of $5,659, 111th in the nation out of 3,143 cities and counties, and Prince's George's had a per capita income of

Average per capita income for the United States was $4,572.