In this article, nonsmooth extensions of the Speed-Gradient (SG) algorithms in differential and finite forms are proposed. The conditions ensuring achievement of the control goal (convergence of the goal function to zero) are established. Furthermore, conditions under which the control goal is achieved in finite time with the use of nonsmooth or discontinuous SG algorithms are obtained. Theoretical results are illustrated by example of nonsmooth energy-based control for a non-affine in control pendulum-like system.