In order to study the complex global dynamics of a series of blackouts in power transmission systems a dynamical model of such a system has been developed. This model includes a simple representation of the dynamical evolution by incorporating the growth of power demand, the engineering response to system failures, and the upgrade of generator capacity. Two types of blackouts have been identified, each having different dynamical properties. One type of blackout involves the loss of load due to transmission lines reaching their load limits but no line outages. The second type of blackout is associated with multiple line outages. The dominance of one type of blackout over the other depends on operational conditions and the proximity of the system to one of its two critical points. The model displays characteristics such as a probability distribution of blackout sizes with power tails similar to that observed in real blackout data from North America.