Willi Kauhsen had previously competed in sportscar racing and founded his team initially in Formula Two in 1976, purchasing championship-winning Renault cars renamed as Kauhsen-Renaults. Despite an encouraging start — with Michel Leclère taking pole at Silverstone in the 1977 Formula Two championship — ongoing modifications to the chassis degraded performance and the team suffered successive failures to qualify. By the end of 1977 Kauhsen had abandoned the Formula Two programme entirely.
Undeterred, Kauhsen pivoted to Formula One for 1979. Having failed to secure the Japanese Kojima chassis, he commissioned his own car during 1978 under the direction of designer Klaus Kapitza, recruited from Ford. The plan was to build a copy of the Lotus 79, the car that had dominated the 1978 championship through its exploitation of ground-effect aerodynamics.
The Kauhsen WK was built around a new chassis with the intent of replicating the Lotus 79's ground-effect concept. Beyond the chassis, the team sourced proven off-the-shelf components: a Cosworth DFV engine, as used by the majority of competitors, and an outdated five-speed Hewland gearbox. Initial testing of the prototype, however, exposed a critical flaw — the designers had failed to account for the variable ride height of the car under braking and acceleration, which prevented the ground effects from functioning correctly.
The team was forced to undertake a full redesign of the car, bringing in drivers Patrick Nève and Harald Ertl to aid development. The redesign consumed much of the team's limited budget in the months preceding the season. Ultimately, the ground-effect concept was abandoned altogether, and the car reverted to the older conventional wing-car layout that had been prevalent before Lotus's innovations.
With funds severely depleted, Kauhsen managed only older-specification Goodyear tyres and was barely able to cover the championship entry fee. The Italian driver Gianfranco Brancatelli was signed to race the car.
The Kauhsen WK004 made its debut at the first race of the 1979 British Formula One season held at Zolder, Belgium, but retired early with engine failure. The car's first World Championship appearance proper was at the Spanish Grand Prix, where Brancatelli qualified as the slowest of the 27 entrants, sitting three seconds off the next competitor. He failed to qualify. At the following Belgian Grand Prix, a broken clutch further hampered the car's pace and Brancatelli again failed to qualify.
Following these two consecutive failures to reach the grid and with no further funding available, Willi Kauhsen withdrew from Formula One and closed the team.
The Kauhsen team's assets, including the WK chassis, were purchased by Italian driver-constructor Arturo Merzario. Giampaolo Dallara then redesigned the Kauhsen WK as the basis for the Merzario A4, retaining the same Cosworth DFV engine and Hewland gearbox combination. Despite Dallara's involvement, the A4 proved even slower than its predecessors and also failed to qualify for every World Championship Grand Prix it entered. The A4's sole racing appearance was the non-championship Dino Ferrari Grand Prix at Imola, where Merzario finished eleventh and last.
The Kauhsen WK thus stands as a cautionary tale of the ground-effect era: a car that attempted to copy the most advanced concept of the time but lacked the engineering resources to execute it properly, leaving its legacy as a chassis that served neither its original team nor its eventual successors in competition.