This paper continues the theoretical investigation of Park and Phillips . We develop an asymptotic theory of regression for multivariate linear models that accommodates integrated processes of diﬀerent orders, nonzero means, drifts, time trends and cointegrated regressors. The framework of analysis is general but has a common architecture that helps to simplify and codify what would otherwise be a myriad of isolated results. A good deal of earlier research by the authors and by others comes within the new framework. Special models of some importance are considered in detail, such as VAR systems with multiple lags and cointegrated variants.