Techniques for supporting communication for different user equipments (UEs) on different system bandwidths are described. In one design, a base station transmits first control information to support communication for at least one first UE on a first system bandwidth and transmits second control information to support communication for at least one second UE on a second system bandwidth, which overlaps the first system bandwidth. The base station transmits data to the first and second UEs on the first and second system bandwidths, respectively. In one design, the base station receives third control information from the first UE(s) and fourth control information from the second UE(s) on a third system bandwidth. The base station receives data from the first UE(s) on the third system bandwidth and receives data from the second UE(s) on a fourth system bandwidth, which overlaps the third system bandwidth.