Environmental factors can stably perturb the epigenome of exposed individuals and even that of their offspring, but the pleiotropic effects of these factors have posed a challenge for understanding the determinants of mitotic or transgenerational inheritance of the epigenetic perturbation. To tackle this problem, we manipulated the epigenetic states of various target genes using a tetracycline-dependent transcription factor. Remarkably, transient manipulation at appropriate times during embryogenesis led to aberrant epigenetic modifications in the ensuing adults regardless of the modification patterns, target gene sequences or locations, and despite lineage-specific epigenetic programming that could reverse the epigenetic perturbation, thus revealing extraordinary malleability of the fetal epigenome, which has implications for ‘metastable epialleles’. However, strong transgenerational inheritance of these perturbations was observed only at transgenes integrated at the Col1a1 locus, where both activating and repressive chromatin modifications were heritable for multiple generations; such a locus is unprecedented. Thus, in our inducible animal models, mitotic inheritance of epigenetic perturbation seems critically dependent on the timing of the perturbation, whereas transgenerational inheritance additionally depends on the location of the perturbation. In contrast, other parameters examined, particularly the chromatin modification pattern and DNA sequence, appear irrelevant.