The existence of market power in the electricity market is a recurrent issue. Measuring and understanding market power practices in the Iberian electricity market turn out to be interesting: though a liberalized market, two integrated firms control 80% of total demand and there is a strong - often direct - intervention of government in the market. For various reasons, among which the difficulty in obtaining reliable, extensive data stands out, market power in the Iberian electricity market has rarely been measured. This work aims to contribute to a better knowledge of the way market power occurs. We calculate the elasticity of residual demand to evaluate the two dominant firm’s market power, using hourly bides in the Spanish spot market for the period July-August 2004 to 2006. Although our approach was highlighted by Frank Wolak work on the electricity sector, we extend it and discuss its constraints. We discuss the results obtained in the light of the evolution of the electricity sector during that period.