Volvo was trying to find a way to advertise and sell more of the new Volvo 343. The car was developed by DAF to become the new car after the DAF 66. When Volvo bought DAF they did some more developing on the car, and then released it as Volvo 343.

A more and more popular motorsport in Sweden was rallycross, so Gunnar Andersson at Volvo Competition Service was given the task to enter the 343 at the rallycross scen. He said that they would make the 343 a winner in three years.

They built a turbocharged car, gave it to Per-Inge Walfridsson in 1977. He was already competing in the Swedish Championship with the Volvo/DAF 66, also built by Volvo CS. In the two final rounds of the championship Walfridsson used the turbocharged 343, with the stock CVT system. And became Swedish Champion in 1977.

1978 Walfridsson and Per Engseth from Norway, was the Volvo R-Team drivers in the 343. The cars had a 1628 cc Volvo/Renault B14 engine  with Garett turbocharger. And put out aprox 245 bhp at 6000 rpm. Walfridsson finished 4^th in the championship, and Engseth 19^th.

Towards the of the 1978 season, Börje Carlsson entered the Volvo R-Team. And he won the Race of Champion in Sweden, that also was broadcast on Swedish tv. Perfect advertisement for the Volvo.

In 1979 Börje Carlsson and Per-Inge Walfridsson raced the Volvo R-Sport 343 in the European, Nordic and Swedish championship. Walfridsson won the Swedish, finished 4^th in the European and 6^th in the Nordic. Carlsson won the Nordic, became 5^th in the Swedish and 7^th in the European.

In the Nordic Championship Per Engseth was back in the Volvo. And finished 2^nd overall.

1980. Four drivers was driving for the Volvo R-Team. Per-Inge Walfridsson, Per Engseth, Börje Carlsson and Anders Hultqvist. Now the cars had manual gearboxes, from Alfa. And this year the Volvo team won almost everything. Walfridsson won the European Championship, Engseth finished 3^rd, Hultqvist 4^th and Carlsson 5^th. Per Engseth also won the Swedish Championship this year.

After the season the Volvo R-Team was cancelled. Gunnar Andersson and Volvo had done what they set out to do. Now it was the private drivers turn to take on the flag, and they did. Anders Hultqvist won the Swedish Championship in 1981 and 1982. Walfridsson finished 2^nd in –82.