The 761 was not a fresh design but rather a development of the March 751. The initial three examples were built up from 751 chassis that had survived the 1975 season, reflecting the financial constraints that shadowed March's Formula One effort throughout this period. Despite its modest origins, the car proved fast enough to challenge at the front when properly driven, and its combination of simplicity and relatively low cost would later make it attractive to privateer teams.
Ronnie Peterson arrived at March for 1976 after becoming disatisfied with the uncompetitive Lotus 77. The 761 gave him a capable if fragile platform, and he qualified on pole at the Dutch Grand Prix and set fastest lap at the Italian Grand Prix before taking the chequered flag at Monza — March's second and last Formula One victory. That win came against the backdrop of an operation running on minimal resources, with Hans-Joachim Stuck as Peterson's works teammate and the cars appearing in varying liveries as race-by-race sponsorship deals were assembled.
A lower-tier entry ran under the March Engines banner for paying drivers Lella Lombardi and Arturo Merzario. By mid-season BMW was pressing Robin Herd to redirect his engineering focus entirely toward the works Formula Two programme, which was falling behind French constructors such as Martini and Elf as well as the new Ralt concern. Peterson scored only one additional point across the rest of the year before moving to Tyrrell for 1977. Despite feeling most at home at March, he acknowledged the team lacked the resources to operate Formula One at a competitive level.
For 1977 the works cars were upgraded and redesignated 761B. March ran a token F1 effort with Rothmans sponsorship for Alex Ribeiro and Ian Scheckter, but the results were inconsequential. Even as the factory programme faded, the 761's affordability and availability made it the car of choice for privateer entrants. Frank Williams, rebuilding his operation after a difficult split with Walter Wolf, acquired a 761 to keep racing while his own car was developed — the car helping to bridge a critical transitional period for what would become Williams Grand Prix Engineering.
Arturo Merzario later attempted to develop his personal 761 into a ground-effect car in collaboration with Simon Hadfield. The project was unsuccessful. At the end of 1977 the March Formula One team's assets and its FOCA membership were sold to ATS, which had recently acquired the Penske cars. Robin Herd was retained as a consultant, placing him in the unusual position of advising on the development of a car derived from his own 1975 design. The resulting 1978 ATS showed traces of contemporary March thinking.
The March 761 represents the last genuinely competitive works Formula One effort from March Engineering. Its single victory at Monza remains one of the more romantic results of the mid-1970s period, a resourceful private constructor defeating well-funded factory teams on one of the fastest circuits on the calendar. The car's subsequent life in privateer hands — carrying Frank Williams through a pivotal rebuilding phase — adds a further layer of historical significance to a design that was unpretentious but effective.