Typical real world tasks such as configuration or design exhibit dynamic aspects which require extending the basic constraint satisfaction framework. In this paper we use the notion of conditional constraint satisfaction (Cond-CSP) as defined by [Mittal and Falkenhainer, 1990] to provide a framework in which these problems can be formulated and solved. It has been shown in [Soininen et al., 1999] that the decision problem for CondCSP is NP-complete similar to standard CSPs. Solving standard CSPs applies various degrees of local consistency to avoid recomputing infeasible branches in the search tree. In a similar manner, we define new types of local consistency aimed at solving conditional CSPs more efficiently. The different algorithms are compared using a series of randomly generated problems.