Low-income residents of Fairfax County and Fairfax City may be eligible for up to $250 in financial aid to help with their fuel and utility bills.

The special fuel and utility assistance program is made available with federal funds, which will be given to eligible households on a first come, first served basis. Applications can be made now through Aug. 31. The program is being carried out by the Fairfax County Area Agency on Aging in cooperation with other county agencies.

People who want to apply for aid must be at or below the federally established annual gross income limits of: $3,713 annual income for a household of one; $4,913 for a household of 2; $6,113 for 3; $7,313 for 4; $8,513 for 5, and $9,713 for a 6-member household. For households larger than six members, add $960 for each additional member to the 6-member limit.

Applicants must have outstanding fuel or utility bills, or have had their utilities shut off or threatened to be turned off, or have been refused delivery of fuel. Also, households that have suffered financial hardship to keep their fuel and utility bills paid in part or whole may be eligible for aid. People who live in a rented house or apartment where their fuel and utility bills were paid through their rent from October 1976 to the present time are not eligible for aid under the program.

When they apply, people must bring proof of income for the period of August 1976 to August 1977 and their paid or unpaid fuel and utility bills from October 1976 to the date of application. They should also bring notices of utility shut-off or refusal to deliver fuel when they apply.

The following agencies will accept applications. Call for an appointment first:

Department of Social Services - Bailey's Crossroads, 671-0246 or 671-6560; Fairfax, 4041 University Drive, 938-5300, Route One, 768-6996 or 768-4744.

Office of Assessments - Fairfax, 691-2511; McLean, 691-2511; Groveton (Alexandria), 691-2511; Franconia, 691-2511.

American Red Cross - 591-8091.

Saunders B. Moon Community Action Association - 360-6041.

Fairfax Community Action Program - 536-3303.

People who are homebound and want to apply for aid should call the Fairfax Red Cross, the Fairfax Community Action Program or the Saunders B. Moon Community Action Association at the numbers listed above. For more information, call 691-3253.