Here is a list of places that let you race old race cars:
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Vintage sports car racing
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Add-Vintage Motors — Restoration shop in Hauser Lake, Idaho
http://www.addvintagemotors.com/
Arch Motor and Manufacturing Co., Ltd.
http://www.archmotor.co.uk/
AS Motorsport
http://www.asmotorsport.co.uk/
Aston Martin Lagonda Limited
http://www.astonmartin.com/
Austin 7 Club
http://www.austin7club.org/
The Automotive Archeologists, Ltd.
http://www.autoarch.com/
Dave Bean Engineering
http://www.davebean.com/
Jack Brabham
http://www.jackbrabham.com/
The Brooklands Society
http://www.brooklands.org.uk/
Chevron Racing
http://www.chevronracing.com/
Cooper Cars
http://www.coopercars.org/
ECTA — East Coast Timing Association — racing at Bonneville and Maxton, North Carolina
http://www.ecta-lsr.com/
Elva Racing Components
http://www.elva.com/
fatto gatto racing
http://www.fattogatto.com/
Fiberglass Sports Cars 1950 to 1965
http://www.fiberglasssportscars.com/
Formula 5000 Registry
http://www.f5000registry.com/
Formula Race Car Club of America
http://www.frcca.com/
Dan Gurney's All American Racers
http://www.allamericanracers.com/
The Goodwood Festival of Speed
http://www.goodwood.co.uk/
HSR — Historic Sports Car Racing, Ltd.
http://www.hsrrace.com/
HSR West — Historic Sports Car Racing West, Inc.
http://www.hsr-westracing.com/
Henry Jones' Vintage Mustang
http://www.historicmustang.com/
Historicracing.org.uk
http://www.historicracing.org.uk/
International Motor Racing Research Center at Watkins Glen
http://www.racingarchives.org/
Lesco Automotive Machine
http://www.4-lesco.com/
Lola Cars International, Ltd.
http://www.lola-group.com/
Lynx Motors International, Ltd. — vintage Jaguar racers
http://www.lynxmotors.co.uk/
Marchives
http://www.marchives.com/
Bruce McLaren Trust
http://www.bruce-mclaren.com/
McLaren International
http://www.mclaren.co.uk/
Tam McPartland's Old Race Car Site
http://www.tamsoldracecarsite.net/
Merlyn Cars — spare parts available from CRD Tool & Engineering
http://www.merlyncars.com/
Morgan Motor Company
http://www.morgan-motor.co.uk/
Stirling Moss
http://www.stirlingmoss.com/
OldRacingCars.com
http://www.oldracingcars.com/
Pebble Beach Concours d'Elegance
http://www.pebblebeachconcours.net/
Portland Historic Races
http://www.portlandhistorics.com/
Race-cars.com — vintage sports racing cars for sale
http://www.race-cars.com/
Race Legends
http://www.racelegends.com/
Ralt Racing Cars
http://www.ralt-racing.co.uk/
Retro Track & Air (UK), Ltd.
http://www.retrotrack.co.uk/
Robin Automotive
http://www.robinautomotive.com/
SascoSports, Inc.
http://www.sascosports.com/
SCCA — Sports Car Club of America
http://www.scca.com/
SCTA — Southern California Timing Association — racing at Bonneville, El Mirage and Muroc
http://www.scta-bni.org/
John Starkey Cars
http://www.johnstarkeycars.com/
SVRA — Sportscar Vintage Racing Association
http://www.svra.com/
Symbolic Motors
http://www.symbolicmotors.com/
Think Fast Ink
http://www.lastopenroad.com/
USFRA — Utah Salt Flats Racing Association — racing at the Bonneville Salt Flats
http://www.saltflats.com/
VARAC — Vintage Auto Racing Association of Canada
http://www.varac.ca/
Victory Lane — "The vintage and historic racing magazine"
http://www.victorylane.com/
Vintage Engineering — McLaren parts
http://www.vintageeng.com/
The Vintage Garage — vintage Lotus racers
http://www.vintagegarage.com/
Vintage Motorsport — "The journal of motor racing history"
http://www.vintagemotorsport.com/
Vintage Racecar Journal
http://www.vintageracecar.com/
VintageRaceCars.com
http://www.vintageracecars.com/
Vintage Sports Car Drivers Association
http://www.vscda.org/
Bob Woodman Tires, Inc. — for vintage sports racing cars
http://www.bobwoodmantires.com/
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Vintage stock car racing
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Living Legends of Auto Racing, Inc.
http://www.livinglegendsofautoracing.com/
North Carolina Auto Racing Hall of Fame
http://www.ncarhof.com/
Northwest Vintage Modified
http://www.nwvintagemodified.com/
Racetorations
http://www.racetorations.com/
Thunderplex
http://www.thunderplex.com/
Vintage Modifieds
http://www.vintagemodifieds.com/
Vintage Oval Track Magazine
http://www.vintageovalracing.com/
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