Capacity constraints on transmissions of electricity are raising an increasing policy concern as electricity markets are integrated around the world. But our understanding of the workings of such markets is still limited. The purpose of this paper is to highlight the impact of transmission capacity constraints and transmission costs on electricity market auctions. In the presence of transmission capacity constraints, the equilibrium is asymmetric even when the suppliers are symmetric in generation capacity and costs. An increase in transmission capacity induces non-monotonic changes in firms' profits. In the presence of transmission constraints and zero transmission costs, an increase in transmission capacity is pro-competitive; in contrast, then the transmission costs are positive, an increase in transmission capacity could be anti-competitive.