The Degradation data provide a useful resource for obtaining reliability information for some highly reliable products and systems. In addition to product/system degradation measurements, it is common nowadays to dynamically record product/system usage as well as other life-affecting environmental variables such as load, amount of use, temperature, and humidity. We refer to these variables as dynamic covariate information. In this paper, we introduce a class of models for analyzing degradation data with dynamic covariate information. We use a general path model with individual random effects to describe degradation paths and a vector time series model to describe the covariate process. Shape restricted splines are used to estimate the effects of dynamic covariates on the degradation process. The unknown parameters in the degradation data model and the covariate process model are estimated by using maximum likelihood. We also describe algorithms for computing an estimate of the lifetime distribution induced by the proposed degradation path model. The proposed methods are illustrated with an application for predicting the life of an organic coating in a complicated dynamic environment (i.e., changing UV spectrum and intensity, temperature, and humidity).