Single-cell RNA-sequencing (scRNA-seq) allows transcript profiling at the level of single cells, enabling cell identity delineation and the study of cell-level heterogeneity of gene expression. Through differential expression (DE) analysis, marker genes can be discovered that define different cell identities, or that are (differentially) associated with a particular developmental process, e.g. the development of a stem cell to a differentiated cell type. First, we show that adopting bulk RNA-seq methods for DE analysis in scRNA-seq data suffers from excess zeros, especially for full-length protocols. We therefore introduce observation weights derived from zero inflated negative binomial (ZINB) models that effectively down-weight excess zeros in the analysis, and unlock bulk RNA-seq tools for DE analysis in single cell applications. Second, we introduce a generalized additive model (GAM) framework for DE analysis downstream of trajectory inference as genes often exhibit nonlinear expression profiles along development. We show how the NB-GAMs provide a powerful approach to assess differences in gene expression along and between lineages of a trajectory.