On Tuesday, shortly before noon, two infants died in a fire that gutted an old frame house in the 3200 block of Ninth Place SE. The house was, according to city officials, not a licensed day-care facility and was part of what they called a growing phenomenon in Washington.

There are about 200 homes in the District of Columbia that are licensed to care for children whose parents work during the day, officials said. But representatives of city agencies and others familiar with the field say that unlicensed day-care homes, like the one on Ninth Place, far outnumber licensed ones, and they say the gap is widening.

These unlicensed homes are often a boon to parents who find themselves unable to afford the more expensive day care at licensed facilities. Many of the former, perhaps most, offer care that is acceptable in every way. But officials said they constitute a growing problem because there is no way to tell whether they are following proper safety procedures.

Fire officials have not determined the cause of the Ninth Place blaze that killed Steven Williams, 5 months old, and Kimberly Nicole Williams, 9 months. They said, however, that they found no fire extinguishers in the two-story frame house. One of the requirements for licensing a home calls for fire extinguishers on every floor.

Capt. James Tate, the fire department's public information officer, said the children who died in the fire on Ninth Place were not related to the people who lived there, and that the children were being cared for during the day. Frances Bowie, head of the D.C. Department of Human Services' licensing and certification office, said the house was not a licensed day-care facility.

Occupants of the house declined to comment yesterday.

"Licensing is a big issue in child care," said Helen Taylor, executive director of the National Child Day Care Association. "People in this city and across the country are concerned."

In a city where there are, proportionately, more working mothers who have children under the age of 6 than anywhere else in the nation, the issue is of special concern.

Taylor said that while the District has one of the strictest licensing laws in the nation, it hasn't enough money and staff to ensure proper enforcement. Unlicensed day-care homes are difficult to detect, she said, and parents are largely unaware that licenses are required, so they generally do not call the city to complain.

Also, the unlicensed homes usually charge less than licensed commercial centers--thus appealing to economically pressed parents with no place else to turn--and often are run by family friends or acquaintances. Thus there is little incentive to report unlicensed facilities.

Last year, subsidized day-care facilities in the city were caring for only 4,708 children, while there were about 34,000 children under age 5 and more than 50,000 working women with at least one school-aged child in Washington.

"It's very difficult to locate everyone who might be providing child-care services in their homes," said Bowie.

Joan Tillman, head of the Mayor's Commission on Early Childhood Development, urged people to call the city when they suspect someone is operating an unlicensed day-care center.

"It's not like you are telling on someone, but it's looking out for the good of the children," she said. "If this is going on in your community, we should know about it. A lot of children are abused by staying in houses without adequate supervision."

Basically, Bowie said, the city's eight-year-old law requires anyone caring for a child, who is not related to them, must be between the ages of 18 and 70, be certified to be in good health, have a clean, wholesome environment with smoke detectors and fire extinguishers on every floor, and keep no more than five children, including their own, who are less than 6 years old. Bowie said she has a staff of five inspectors and a clerical worker charged with surveying the city for violations and helping applicants secure licenses. It's not enough, she says.

She said the economy appears to be forcing more mothers to work and more people to supplement their incomes by taking care of children. The number of day-care homes, both licensed and unlicensed, is increasing.

Mary Keyserling, an economist and local authority on child care, said the number of mothers who have had to go to work in the last decade is "staggering." She said the result has been a new abundance of children who must be cared for during the day.

Keyserling said Washington has done better than most American cities in providing day-care programs, but added that the recession and Reagan administration budget cuts are undermining the District's programs.