Cellular decision making in differentiation, proliferation, or cell death is mediated by molecular signaling processes, which control the regulation and expression of genes. Vice versa, the expression of genes can trigger the activity of signaling pathways. We introduce and describe a statistical method called Dynamic Nested Effects Model (D-NEM) for analyzing the temporal interplay of cell signaling and gene expression. D-NEMs are Bayesian models of signal propagation in a network. They decompose observed time delays of multiple step signaling processes into single steps. Time delays are assumed to be exponentially distributed. Rate constants of signal propagation are model parameters, whose joint posterior distribution is assessed via Gibbs sampling. They hold information on the interplay of different forms of biological signal propagation. Molecular signaling in the cytoplasm acts at high rates, direct signal propagation via transcription and translation act at intermediate rates, while secondary effects operate at low rates. D-NEMs allow the dissection of biological processes into signaling and expression events, and analysis of cellular signal flow. An application of D-NEMs to embryonic stem cell development in mice reveals a feed-forward loop dominated network, which stabilizes the differentiated state of cells and points to Nanog as the key sensitizer of stem cells for differentiation stimuli.