BIRD-SELLERS do a brisk business in the marketplace of this resort city on the Black Sea. They sell many species, but perhaps no other merchants can match the three who sell Australian parakeets to eager children while parents dig into their ostentatious Levi's for the $20.40 asking price.

What is new about this scene is not the birds from Down Under nor the dungarees from America. The oddity is that parents and children are taking family vacations in Sochi. Thousands of families are here this month, and I am told this is something new and wholesome.

Family vacations are hard to arrange in a land where both parents mormally work and have different kind of seniority and vacation privileges. But the family vacation is a force to be reckoned with, having the approval of increasing numbers of senior officials - who many or may not take them themselves. One S. Shalayev, secretary of the all-union Central Council of Trade Unions, writing in Izvestia last year, said on behalf of his council: "Not only do we want mothers to vacation with their children, we want whole families to do so, since we believe that this is most sensible, moral and useful from all points of view."

He said that since 1971, the trade unions, which have enormous leverage in the Soviet Union, have been trying to imporve this aspect of their members' lives. The effort seems to be bearing fruit in Sochi. Our Intourist guide, a man with impeccable English and an encylopedic knowledge of the area's history, repeatedly showed us sanitariums and hotels where family-style wings were being added to accommodate the new fashion.

THERE ARE FEW human relationship more dynamic than those of Russian parents and their children. Emotion flows back and forth like tides in the Bay of Fundy, reaching high-water marks in an instant, then rolling back the other way. Several days her offered wonderful examples of the stormy, forgiving nature of the relationship. Some sequences from the beach and the promenade:

Click . Spindly litle boy in ruober sandals, short pants with suspenders, and a little white suncap perched on his towhead; he is strolling with his big mama along the asphalt ribbon that goes behind the seawall. They pass a kiosk with various items in the window. "Mama, can I have a hat?" No response. "A bat, can I have a hat?" They go on, the little one dragging on the big hand. Now he is looking back over his shoulder and tears are rolling down his cheeks. They go on like this for another 50 yards and then mama says, sweetly, "Of course, Volya," and they swing back, heading for the kiosk.

Click . "Come out now, out of the water." The two little boys peer with huge eyes at their mama. And stay in the water: "Come out, you two, you'll get too cold. You'll get too much sun. You need to rest here with me." They keep playing. Now mama is on her feet, wading into the water. There is a sharp smack of large hand on young flesh, a howl, fierce tears . . . then silence. She is back on her wooden pallet on the pebble beach and the boychiks are in the water. Everybody is smiling.

Click . A man is lying in the grass on the tree-shaded bank behind the seawall promenade. He is wearing the vacation uniform for the Soviet male - dark trousers, synthetic opennecked short-sleeved light shirt, socks and sandals. He is snoozing, hand thrown over his face. A girl of about 10 walks over and plump ! drops square on his ample midriff. He struggles up gasping, face blanched, showing confusion, hurt, and anger. I am embarrassed watching, knowing an explosive scolding is coming. He grabs and hugs the girl with a big grin on his face.

THE PRIVATE MARKET is alive with animals of all kinds in all kinds of cages. There are piglets in little wooden cages, rabbits in a small cardboard box, puppies in a tiny pen. A gnarled old man beckoned me with an arthritic hand to look at his briefcase. On the scarred leather in initials R.R.T. were barely visible near the tarnished lock. It was the kind of expensive case you see on the Metro, making the run from Farragut Square to the federal courhouse in the grip of a tanned, handsome pracitioner. I looked inside. A rooster and three hens were nestled there.

ONE AFTERNOON, my two journallist colleagues and I found a good restaurant and made a reservation for 8 p.m. "We're American correspondents," said one of uss to the waitress taking the reservation. She smiled as though that piece of information impressed her.

When we arrived at the appointed hour, we were shown to a table for four. The order quickly taken, wine and an appetizer arrived and the band struck up "Blue Moon." Then a man walked up in the crowded restaurant and asked if he could sit with us.

A gaunt fellow, he resembled Ichabod Crane, and like him, turned out to be a school teacher. It happened, as these things sometimes do, that he spoke good English and wanted to learn about his tablemates. We were more interested in him, and asked about his life.

He told us that he comes to Sochi each year for a rest. He didn't like the heat, however, nor did he enjoy swimming, which seemed strange to us. Perhaps it explained his unredeemed pallor in a city that boasts 200 days of sun and where we found that it wasn't hard to get pretty well burned just walking around.

"Tell me an anecdote," he suggested. We were fresh out, so we asked him for some. He said he would think of one, and then he got up and began tablehopping around the restaurant and dancing with some of the girls who were sitting here and there. He seemed to get along well with the Sochi just once a year.

After a while, he just sort of faded away and we never saw him again.