This article proposes two types of degradation models that are suitable for describing multivariate degrading systems subject to time‐variant covariates and imperfect maintenance activities. A multivariate Wiener process is constructed as a baseline model, on top of which two types of models are developed to meaningfully characterize the time‐variant covariates and imperfect maintenance effects. The underlying difference between the two models lies in the way of capturing the influences of covariates and maintenance: The first model reflects these impacts 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, two particular imperfect maintenance models are presented, which 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.