This paper studies the cointegration properties of vector autoregressive models having a block triangular structure, where unit roots may appear in either the marginal or conditional subsystems, or both. In the former case, the conventional stability analysis of dynamic systems is extended to deal with integrated exogenous variables. The concept of target relations incorporates economic equilibrium relationships into the model, with observed cointegrating vectors being interpreted as linear combinations of these. Unstable models may be classified as containing insufficient or inconsistent targets, according to a rank condition on the sum of the lag coefficient matrices. Copyright 1991 by Royal Economic Society.