Identifying causal relationship is an often desired, but difficult, task, and generally only possible under specific assumptions. In this paper we are considering the task of identifying causal relationships between entities that have a temporal axis, as for example continuous measurements of different components within a complex machine. We introduce a locally linear model class that allows us to recover causal relationships, assuming that the process is locally linear, that we have access to observations in diverse environments and that the causal structure is invariant across the different environments. We validate the model in a theoretical and two experimental settings.