There is a growing interest in languages that combine probabilistic models with logic to represent complex domains involving uncertainty. Causal probabilistic logic (CP-logic), which has been designed to model causal processes, is such a probabilistic logic language. This paper investigates inference algorithms for CP-logic; these are crucial for developing learning algorithms. It proposes a new CP-logic inference method based on contextual variable elimination and compares this method to variable elimination and to methods based on binary decision diagrams. ; status: published