We investigate the range of inflationary universe models driven by scalar fields possessing a general interaction potential of the form $V(��) = V_0 ��^n \exp(-����^m)$. Power-law, de Sitter and intermediate inflationary universes emerge as special cases together with several new varieties of inflation. Analysing the behaviour of these models at the extrema of $��$ we derive sufficient constraints on the $m$ - $n$ parameter space such that inflation may occur as both an early and late-time phenomenon. We also compute the scalar and tensor perturbations produced in the model and compare these results with recent observations.

19 Pages, LATEX.