Previously, stability inequalities in viscoplasticity appear to have been applied primarily to cases in which the associated flow rule is satisfied. Here, a stability inequality is formulated for a simple example of a non-associated viscoplastic constitutive model. The inequality ensures that a certain Jacobian matrix is Hurwitz. The main mathematical difficulty in non-associated models is the presence of a nonsymmetric vector dyadic product in the Jacobian matrix. In the current paper, to overcome this difficulty, general upper and lower bounds on the real parts of the eigenvalues of such products are derived and applied to the Jacobian matrix of interest. A relatively “sharp” stability inequality is first obtained in a complicated form. At some loss in sharpness, it is simplified to furnish a second inequality purely involving the condition number of a “flow compliance” matrix. Applications are given which correspond to an isotropic associated flow model and to a transversely isotropic non-associated model.