When transmission constraints limit the flow of power in art electric network, there are likely to be strong interaction effects across different parts of the system. A model of imperfect competition with strategic interactions in an electricity transmission network illustrates a possible exercise of market power that differs from the usual analysis of imperfect competition in more familiar product markets. Large firms could exercise horizontal market power by increasing their own production, lowering some prices, and exploiting the necessary feasibility constraints in the network to foreclose competition from others. This behavior depends on the special properties of electric networks, and reinforces the need for market analysis with more realistic network models.