Induced pluripotent stem cells (iPSCs) are capable of providing an unlimited source of cells from all three germ layers and germ cells. The derivation and usage of iPSCs from various animal models may facilitate stem cell-based therapy, gene-modified animal production, and evolutionary studies assessing interspecies differences. However, there is a lack of species-wide methods for deriving iPSCs, in particular by means of non-viral and non-transgene-integrating (NTI) approaches. Here, we demonstrate the iPSC derivation from somatic fibroblasts of multiple mammalian species from three different taxonomic orders, including the common marmoset (Callithrix jacchus) in Primates, the dog (Canis lupus familiaris) in Carnivora, and the pig (Sus scrofa) in Cetartiodactyla, by combinatorial usage of chemical compounds and NTI episomal vectors. Interestingly, the fibroblasts temporarily acquired a neural stem cell-like state during the reprogramming. Collectively, our method, robustly applicable to various species, holds a great potential for facilitating stem cell-based research using various animals in Mammalia.