Thirty-four local firms, mostly in the computer technology business, have made the list of America's 500 fastest-growing private companies compiled annually by Inc. magazine.

Of those firms, most are in Virginia, which had 32 of the top 500, third in the nation behind California, with 86 companies, and Texas, with 38, according to a press release accompanying the survey in the magazine's December issue.

Inc., a magazine geared toward entrepreneurs and small and medium-size businesses, said its third annual survey indicates "the class of 1984 is the youngest, fastest-growing -- and by far the most productive -- in the history of the ranking." To be considered for the listing -- which ranks businesses according to percentage increase in sales from fiscal 1979 through fiscal 1983 -- a firm had to be privately held, at least five years old, and have shown sales in 1979 of between $100,000 and $25 million.

Heading the list is Pedus International, a Los Angeles building maintenance and security services firm. Sales at Pedus jumped 15,707 percent between 1979 and 1983, from $383,000 to $60.54 million.

The local leader is VCA Corp., a Vienna computer service firm, listed as No. 12. VCA's sales increased 6,927 percent over the period, from $114,000 to $8.03 million.

The next fastest-growing local company, ranked 17, is Taurio Corp., an Alexandria firm that provides engineering training and services primarily for the Defense Department. In September, General Physics Corp. in Columbia announced it would acquire Taurio.

Ranked 32 is American Leisure Industries Inc., a Lanham travel company. DataStore Associates Inc., a computer retail store in Vienna, ranks close behind at 35. XMCO Inc., a McLean firm that provides defense-oriented professional services, is 37.

Sigal Construction Inc. of Washington is ranked 51, and Systems, Research & Applications Corp., a Vienna computer and management services company, is ranked 60. A data processing firm in Fairfax, Vanguard Technologies Corp., is listed at 66.

Others include Creative Management Systems Inc., a McLean software firm, 85; Moss Brown Co., an Alexandria outdoor-gear store, 89; Maxima Corp., a Bethesda information technology service, 98; and Management Consulting & Research Inc., a Falls Church defense consultant, 109.

Comsel Corp., a Vienna computer firm, is 136; Columbia Woodworking Inc. of Washington, 152; Meridian Corp., a Falls Church research and development firm, 172; Resource Consultants Inc. of McLean, 195; Hanley-Wood, a Washington magazine publisher, 206; Viar and Co. Inc., an Alexandria management services company, 222; Triton Corp., a Washington consultant, 233; and National Trade Productions, an Alexandria marketing firm, 243.

Metrocall of Delaware, an Alexandria cellular phone company, is ranked 254; RSO, a Laurel nuclear safety equipment firm, 270; P E Systems Inc., an Alexandria communications company, 275; Monegon Ltd., a Rockville energy firm, 276; Bruce W. Eberle & Assoc., a Vienna direct marketing agency, 280; Sage Systems Inc., a Rockville software company, 284; Dynamic Systems Inc., a McLean engineering consultant, 323; and Electro Mechanical Design in Gaithersburg, 326.

Booth Organization, a Rockville building maintenance firm, is 342; Computer Science Press Inc. of Rockville, 351; Wild and Wooly Needlecrafts, of Falls Church, 400; Systems & Applied Sciences Corp., a Vienna software company, 426; Comsearch, a Reston telecommunications engineering firm, 431; Miller Oil in Norfolk, 469; and Marine Structural Applications Inc., a Dumfries, Va., marine contractor, 484.