Induced pluripotent stem cells (iPSCs) are regarded as a central tool to understand human biology in health and disease. Similarly, iPSCs from non-human primates should be a central tool to understand human evolution, in particular for assessing the conservation of regulatory networks in iPSC models. Here, we have generated human, gorilla, bonobo and cynomolgus monkey iPSCs and assess their usefulness in such a framework. We show that these cells are well comparable in their differentiation potential and are generally similar to human, cynomolgus and rhesus monkey embryonic stem cells (ESCs). RNA sequencing reveals that expression differences among clones, individuals and stem cell type are all of very similar magnitude within a species. In contrast, expression differences between closely related primate species are three times larger and most genes show significant expression differences among the analyzed species. However, pseudogenes differ more than twice as much, suggesting that evolution of expression levels in primate stem cells is rapid, but constrained. These patterns in pluripotent stem cells are comparable to those found in other tissues except testis. Hence, primate iPSCs reveal insights into general primate gene expression evolution and should provide a rich source to identify conserved and species-specific gene expression patterns for cellular phenotypes.