THERE ARE MANY people who are afraid to fly, and psychiatrists and hypnotists are now holding courses to rid these men and women of their fears.

While a great deal of attention is being paid to the problem, there are still other people who are only afraid to fly with children (not their own). Fear of flying with children has been named "half-fare phobia," by Prof. Heinrich Applebaum, who is the only one doing work in this field.

"Most of my patients are closet half-fare phobics," he told me. "They are afraid to admit they can't stand children on airplanes. These people don't hate children. They just freeze up when they have to sit next to one."

"How do you treat them?" I asked the professor.

He took me into a large room that looked exactly like the tourist-class cabin of a 727.

"We simulate the exact conditions of a flight," Applebaum said.

In the cabin were 33 men and women, all Applebaum's patients.

Most of them appeared to be very normal. Some were reading books, others were knitting, and a few were watching the stewardesses' hips as they swung up and down the aisles.

Suddenly Applebaum pushed a button and two dozen mothers and their children, ranging from babies to 12 years, rushed into the cabin from a door up in front.

The older children, carrying toys, ran down the aisles, climbing over the patients to "get the seat by the window." The mothers with their babies and their tote bags full of formulas and diapers sat down next to the patients.

"Where do you get the mothers and children?" I asked Applebaum.

"I pay them $4 an hour," the professor said. "They love it because it gives them a chance to get out of the house."

I noticed a remarkable change taking place among Applebaum's patients. Some were gripping the armrests for dear life. Others were perspiring, a few were hyperventilating and three were upchucking.

Applebaum went to the front of the cabin. He held a pocket watch and chain in front of him and swung it back and forth.

"Keep looking at this watch," he said. "Relax. Let your mind pay attention only to what I am saying. You have nothing to fear from the child sitting in back of you. If he hits you on the head it will not hurt you. If the little girl in front of you sticks her tongue out at you, do not stick your tongue out at her. You will only encourage her.

"If the mother next to you starts to change her babys diaper on the floor, stare at the FASTEN SEAT BELT sign. Do not notice what is going on around you. Think beautiful thoughts - you are on a singles' cruise or you are sitting in an 'R'-rated movie where no children are allowed. Relax. Lift your hands off the armrests. Do not look to the right or left. In a few hours you will be safe in your office or home."

Some patients were responding while others were fighting to get out of the cabin.

"How many treatments do they have to have before they overcome their fear of flying with children?" I asked.