This paper considers code construction for arbitrar̃ discrete memoryless compound multiple access channels (MACs with common information. This class of channels includes a MA with/without common messages or with partially cooperating encoders. A construction method of code ensem bles based on coset codes is proposed for these channels. Assuming joint maximurn likelihood decoding, the performance of the proposed code ensem ble is analyzed by deriving error exponents. A condition is shown such that codes achieve the capacity region on average. The result obtained here reduces to the result of Slepian and Wolf or other conventional works if restricted to a single MAC. A combination of good linear codes gives capacity achieving codes for compound MACs with common messages or with partially cooperating encoders.