EDITOR'S NOTE: As the Soviet Union stumbles toward a market economy, millionaires and paupers are appearing in a society once called classless. This article, fourth of a series on rich and poor in the U.S.S.R., looks at a family in Uzbekistan, Central Asia, one of the poorest Soviet regions.

Undated (AP) _ By ANN IMSE Associated Press Writer

AKYAR, U.S.S.R. (AP) - In the 104-degree heat of an Uzbek summer, dust seeps into every cranny of the Azamovi family's life.

Dust coats the corrugated tin roof and mud walls of the four-room house that shelters 17 people; dulls the colors of cotton mats piled on the rough plank veranda, ready to be spread for the next meal.

It covers the bare feet and round faces of the children, the iron kettle and ashes of a cooking fire in the lean-to kitchen.

A daughter-in-law of Markhabur Azamovi, the matriarch, leans to rinse her newly washed hair under the only spigot, then dumps the pan of soapy water into the open sewer that runs through the yard.

The Central Asian republics of Uzbekistan, Tadzhikistan, Kirghizia and Turkmenia are the poorest parts of the Soviet Union.

Mikhail S. Gorbachev's reforms may have shaken the foundations of Kremlin power, but they are just starting to touch this remote valley a few hundred miles from Afghanistan and China.

The predominantly Muslim people of Central Asia are proud of their ancient culture and have preserved much of their way of life through seven decades of Soviet rule.

Many do not share an outsider's view of poverty. Saidazim, 21, the youngest of Markhabur's sons, reacted with surprise to a question about it.

''We're not poor,'' he said. ''We have everything we need.''

Families are large in Uzbekistan, and the average worker supports seven people. The 1989 census found 43 percent of the population living below the poverty level.

Soviet statistics put infant mortality at four times the U.S. rate, but local doctors and U.S. experts say the reality is closer to six times.

Virtually all the water in Uzbekistan is contaminated with fecal matter, contributing to high rates of hepatitis, republic health officials say. In some areas, only one-quarter of the people are on sewer systems.

Pravda, the Communist Party daily, reported in 1989 that unemployment had reached 23 percent in the republic.

Residents of Akyar deny that many people are out of work. They suggest officials counted mothers who stay home with their children, every student over age 16 and thousands of people employed outside state-run businesses.

Those workers are ''operating very profitably on the 'second' economy'' of unofficial jobs and black-market deals, said Murray Feshbach, a specialist in Soviet affairs at Georgetown University in Washington, D.C.

He said many Uzbeks are involved in the still largely illegal trade of privately transporting vegetables to Moscow farmers' markets for sale at high prices. Others use their own cars as taxis, earning more in a few hours than a factory would pay in a month.

Markhabur Azamovi, her four sons, three daughters-in-law, daughter and eight grandchildren live in the house, which sits in a high-walled compound.

Six of the eight young adults have jobs, mostly planting and harvesting vegetables on the surrounding collective farm.

Their salaries total 1,000 rubles a month, about $36 at the tourist exchange rate, and it would take all their pay for five months to buy a cow.

Every week, the famly buys two kilograms of meat, about 4 1/2 pounds, which works out to two-thirds of an ounce daily per person.

They have a small corn patch and a few fruit trees in the compound. A few chickens peck in the dust and, on a recent day, mud bricks for a new outhouse were drying in the sun.

Inside the thick, cooling walls of the house, more mats, a pair of hammered tin chests and six painted Russian trays furnish the room shared by the grandmother and her youngest son and daughter.

Tucked into nooks in the whitewashed mud walls are a television and half- size refrigerator. Extension cords strung across the ceiling serve as wiring.

Saidazim, the youngest son, dressed in torn pants, dust-covered sandals and a square Muslim cap, offered two American visitors a bowl of apricots. He said they should toss the pits into the garden.

One of the grandchildren dashed after the pits, cracked them open with a rock and gulped down the inner seed.

''They don't take care of themselves or their children,'' said Dr. Shavkat Sabirov, an Uzbek physician who went along on the visit. He said all the children had rickets, a vitamin deficiency caused by poor diet.

The Azamovi family's immediate problem was to assemble the food for Saidazim's forthcoming wedding feast: a sheep, two sacks of rice, four sacks of flour and liters of oil.

A sheep alone costs 1,000 rubles, a month's pay for the family, but the doctor said they would manage without complaint.

''Even a man who's dying would say everything is fine,'' he said. ''It's the Uzbek way, the Muslim way.''