The behavior of a model of single-crystal strain-gradient viscoplasticity is investigated. The model is an extension of a rate-independent version, and includes a new hardening relation that has recently been proposed in the small-deformation context (Gurtin and Reddy, 2014), and which accounts for slip-system interactions due to self and latent hardening. Energetic and dissipative effects, each with its corresponding length scale, are included. Numerical results are presented for a single crystal with single and multiple slip systems, as well as an ensemble of grains. These results provide a clear illustration of the effects of accounting for slip-system interactions.