The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes However, their application is complicated due to the unavailability of the multivariate density function and so likehhood-based methods remain far from providing a complete and flexible framework kit inference In this article we develop inferentially practical likehhood-based methods for fitting max-stable processes derived from a composite-likehhood approach The procedure is sufficiently reliable and versatile to permit the simultaneous modeling of marginal and dependence parameters in the spatial context at a moderate computational cost The utility of this methodology is examined via simulation. and illustrated by the analysts of United States precipitation extremes