We examine the exercise of market power in California's power market in 1998 2000, with a focus on its day-ahead energy market and its five non-utility thermal generating companies. Our goal is to assess whether the hourly bids of market participants, together with information on thermal unit characteristics and power output, suggest that the five suppliers were behaving in line with Nash supply function competition, bidding close to their marginal costs or restraining quantities relative to the Nash level. The analysis of residual demand inverse elasticities suggests that the five thermal generators had an incentive to exercise unilateral market power that was not always fully exploited. A comparison of market-clearing prices, estimated marginal costs and marginal revenues finds that firm conduct was broadly consistent with Nash supply function competition or more competitive than Nash behavior in most of our sample.