Among the most common purposes are the tracking of reference signals and the rejection of disturbance signals in the face of uncertainties. The related design problem is called the "robust regulation problem." Here we investigate the tradeoff between the robust regulation constraint and the requirement of robust stability with respect to perturbations in the normalized coprime factors of the plant. We use an approach in terms of subspace-valued functions associated to plant and controller. In this way, necessary and sufficient conditions for robust regulation with robust stability can be related to a simple geometric property.