Researchers who study student acceptance of evolution rely on surveys that are designed to measure evolution acceptance. It is important for these surveys to measure evolution acceptance accurately and in isolation from other constructs, so that researchers can accurately determine what leads to low acceptance. The Inventory of Student Evolution Acceptance (I-SEA) and the Generalized Acceptance of EvolutioN Evaluation (GAENE) are two surveys that were developed to improve upon the limitations of earlier surveys. Yet neither survey has been extensively tested for response process validity, which can assess the extent to which students use constructs other than their acceptance of evolution to answer survey items. In this study, we examined the response-process validity of the I-SEA and GAENE by conducting cognitive interviews with 60 undergraduate students. Interviews revealed that both surveys retain certain response-process issues. The I-SEA conflated knowledge about and acceptance of evolution for a subset of students. The GAENE measured evolution acceptance inconsistently because students interpreted "evolution" in different ways; it also measured willingness to advocate for evolution in addition to acceptance. Researchers can use these findings to better inform their survey choice when designing future studies, and to further improve the measurement of evolution acceptance.