A new model of molecular evolution is introduced that allows for heterogeneous rates across the sequence positions. The development of this model was motivated by two issues: first, a number of studies have shown that the positions in a DNA sequence evolve at different rates, and second, it has been shown that not accounting for this heterogeneity can lead to biased estimates of evolutionary parameters. The authors generalize the Markovian model of molecular evolution to allow for heterogeneous rates and explore some of the consequences of such a model. In particular, they quantify the biases incurred by incorrectly assuming an equal-rate model and consider what can be learned about evolutionary parameters under a heterogeneous model.