We develop regression methods for inference on conditional quantiles of time‐to‐transition in multistate processes. Special cases include survival, recurrent event, semicompeting, and competing risk data. We use an ad hoc representation of the underlying stochastic process, in conjunction with methods for censored quantile regression. In a simulation study, we demonstrate that the proposed approach has a superior finite sample performance over simple methods for censored quantile regression, which naively assume independence between states, and over methods for competing risks, even when the latter are applied to competing risk data settings. We apply our approach to data on hospital‐acquired infections in cirrhotic patients, showing a quantile‐dependent effect of catheterization on time to infection.