  We study the category pro-SSet of pro-simplicial sets, which arises in etale
homotopy theory, shape theory, and pro-finite completion. We establish a model
structure on pro-SSet so that it is possible to do homotopy theory in this
category. This model structure is closely related to the strict structure of
Edwards and Hastings. In order to understand the notion of homotopy groups for
pro-spaces we use local systems on pro-spaces. We also give several alternative
descriptions of weak equivalences, including a cohomological characterization.
We outline dual constructions for ind-spaces.
