In the multisensor sequential change detection problem, a disruption occurs in an environment monitored by multiple sensors. This disruption induces a change in the observations of an unknown subset of sensors. In the Byzantine version of this problem, which is the focus of this work, it is further assumed that the postulated change-point model may be misspecified for an unknown subset of sensors. The problem then is to detect the change quickly and reliably, for any possible subset of affected sensors, even if the misspecified sensors are controlled by an adversary. Given a user-specified upper bound on the number of compromised sensors, we propose and study three families of sequential change-detection rules for this problem. These are designed and evaluated under a generalization of Lorden's criterion, where conditional expected detection delay and expected time to false alarm are both computed in the worst-case scenario for the compromised sensors. The first-order asymptotic performance of these procedures is characterized as the worst-case false alarm rate goes to 0. The insights from these theoretical results are corroborated by a simulation study.