Continuous changepoint data may exhibit one of two types of transitions: gradual or abrupt. Modeling the trend for such data is challenging in the presence of discontinuous derivatives. Further complications arise when we have (1) longitudinal data, and (2) samples which come from two potential populations: one with a gradual transition, and the other abrupt. Bent-cable regression is an appealing statistical tool to model such data due to the model’s flexibility and greatly interpretable regression coefficients. We extend bent-cable methodology for longitudinal data to account for both gradual and abrupt transitions. We describe explicitly the computationally intensive Bayesian implementations; and demonstrate our methodology by a simulation study, and with two applications: (1) assessing the transition to early hypothermia in a rat model, and (2) understanding CFC-11 trends monitored globally.