In this article, we develop two degradation models to characterize multivariate degrading systems subject to time-variant covariates and imperfect maintenance activities. We first construct a multivariate Wiener process to serve as a baseline model, on top of which two types of models are developed to meaningfully describe the time-variant covariates and imperfect maintenance effects. The underlying difference between the two models lies in the way of formulating the impacts of covariates and maintenance: The first model reflects these influences in the degradation rates/paths directly, whereas the second one describes the impacts by modifying the time scales governing the degradation processes. In each model, we present two particular imperfect maintenance models that differ in the extent of reduction in degradation level or virtual age. The two degradation models are then compared in certain special cases. The proposed multivariate degradation models pertain to complex industrial systems whose health deterioration can be characterized by multiple performance characteristics and can be altered or affected by maintenance activities and operating/environmental conditions.