We present a number of new, exact scalar field cosmologies where the potential consists of two or more exponential terms. Such potentials are motivated by supergravity or superstring models formulated in higher dimensional spacetimes that have been compactified to (3+1)-dimensions. We have found solutions in both curved and flat Robertson Walker spacetimes. These models have a diverse range of properties and often possess several distinct phases, with a smooth transition between ordinary and

more »

... lationary expansion. While exponential potentials typically produce powerlaw inflation, we find models where the inflationary period contains eras of both powerlaw and exponential growth.