New York City's response to the demand for shelter has consistently been adequate. The city's homeless population is estimated at 35,000, including 11,000 members of homeless families, of whom almost 7,625 are children. The City's Human Resources Administration (HRA) has routinely failed to provide temporary emergency shelter for homeless families. This report focuses on HRA's main, and until recently, only emergency welfare office, the Emergency Assistance Unit (EAU). It is the office where homeless families in need of shelter are directed when HRA's neighborhood income maintenance centers are closed, in the evenings and on weekends. A group of volunteer observers monitored the EAU on eight consecutive weekends in September through November 1984. During that time scores of homeless families were denied placement in temporary shelter when the supply of shelter space to which HRA had access was exhausted. Children and their mothers often had to sleep on the EAU floor. Space is most limited on weekends. Although HRA provides shelter to all homeless men and women who have no children, the agency refuses to acknowledge any similar obligation to homeless families that include children. HRA's has heedlessly neglected the crisis encountered by homeless families with children. Recommendations for improving the housing situation are offered. An appendix provides the testimony of Robert M. Hayes, a lawyer for the Coalition for the Homeless, before the House Subcommittee on Intergovernmental Relations and Human Resources Committee on Government Operations, November 20, 1984. (BJV)