This paper provides insight into the time-varying relation between electricity futures prices and fundamentals in the form of contract prices for fossil fuels. As supply curves are not constant and different producers have different marginal costs of production, we argue that the relation between the prices of electricity futures and those of underlying fundamentals such as natural gas, coal and emission rights varies over time. We test this view by applying a model that linearly relates electricity futures prices to the marginal costs of production, and calculate the loglikelihood of different time-varying and constant specifications of the coefficients. To do so, we formulate the model in state-space form and apply the Kalman filter to observe the dynamics of the coefficients. We analyze historical prices of futures contracts with different delivery periods (calendar year and seasons, peak and off-peak) from Germany and the United Kingdom. The results indicate that analysts should choose a time-varying specification to relate the futures price of power to the prices of underlying fundamentals.