The structure of incremental constitutive equations in multi-surface plasticity is discussed with respect to different choices of state and control variables. The state and control variables can combine stresses and strains as long as they are decomposed into energy-conjugate parts. A general uniqueness condition is established for non-associated flow rules and any choice of control variables. Furthermore, proper tangent constitutive matrices are given within each loading/unloading region. The theory is demonstrated in a simple example involving Tresca's yield condition