Mixed finite element formulations give rise to large, sparse, block linear systems of equations, the solution of which is often sought via a preconditioned iterative technique. In this work we present a general analysis of block-preconditioners based on the stability conditions inherited from the formulation of the finite element method (the Babuška-Brezzi, or inf-sup, conditions). The analysis is motivated by the notions of norm-equivalence and field-of-values-equivalence of matrices. In par...