Comparative biology builds up systematic knowledge of the diversity of life, across evolutionary lineages and levels of organization, starting with evidence from a sparse sample of model organisms. In developmental biology, a key obstacle to the growth of comparative approaches is that the concept of homology is not very well defined for levels of organization that are intermediate between individual genes and morphological characters. In this paper, we investigate what it means for ontogenetic processes to be homologous, focusing specifically on (...) the examples of insect segmentation and vertebrate somitogenesis. These processes can be homologous without homology of the underlying genes or gene networks, since the latter can diverge over evolutionary time, while the dynamics of the process remain the same. Ontogenetic processes like these therefore constitute a dissociable level and distinctive unit of comparison requiring their own specific criteria of homology. In addition, such processes are typically complex and nonlinear, such that their rigorous description and comparison not only requires observation and experimentation, but also dynamical modeling. We propose six criteria of process homology, combining recognized indicators with novel ones derived from dynamical systems modeling. We show how these criteria apply to animal segmentation and other ontogenetic processes. We conclude by situating our proposed dynamical framework for homology of process in relation to similar research programs, such as process structuralism and developmental approaches to morphological homology. (shrink)