The first step toward development a "nonsmooth" version of Speed-Gradient (SG) method is made. As a basis for formal approach the Hadamard subdifferential and set-valued analysis are chosen. Nonsmooth versions of SG-algorithm in differential and finite form are formulated. Conditions for the control goal achievement are proposed. The results are illustrated by an example of asymptotic minimization of the max-norm for a second order linear system.