We present single-cell clustering using bifurcation analysis (SCUBA), a novel computational method for extracting lineage relationships from single-cell gene expression data and modeling the dynamic changes associated with cell differentiation. SCUBA draws techniques from nonlinear dynamics and stochastic differential equation theories, providing a systematic framework for modeling complex processes involving multilineage specifications. By applying SCUBA to analyze two complementary, publicly available datasets we successfully reconstructed the cellular hierarchy during early development of mouse embryos, modeled the dynamic changes in gene expression patterns, and predicted the effects of perturbing key transcriptional regulators on inducing lineage biases. The results were robust with respect to experimental platform differences between RT-PCR and RNA sequencing. We selectively tested our predictions in Nanog mutants and found good agreement between SCUBA predictions and the experimental data. We further extended the utility of SCUBA by developing a method to reconstruct missing temporal-order information from a typical single-cell dataset. Analysis of a hematopoietic dataset suggests that our method is effective for reconstructing gene expression dynamics during human B-cell development. In summary, SCUBA provides a useful single-cell data analysis tool that is well-suited for the investigation of developmental processes.