The complex multivariate multiunit problem formulation of analyzing the effect of recycles on the dynamics of chemical process plants is considered in this Note. Based on the notion of exchange plants and results on conservation matrices, the effect of connections, such as recycles and external sources, such as chemical reaction, heating/cooling etc. is analysed. It has been found that exchange plants are not unstable, regardless of the connections of their operating units. If constant total flow is maintained through each unit then an increase of all kinds of connections including recycles at the expense of an external stream may move the eigenvalues of the plant towards the instability region. This effect can cause stable nonexchange plants to become unstable.