Summary: ``The main purpose of this paper is to generalize the Banach-Steinhaus theorem in locally convex spaces for $\sigma$-locally Lipschitzian operators established by S. Lahrech\ [Miskolc Math. Notes {\bf 6} (2005), no.~1, 43--45; MR2148843 (2006a:46007)] to $\sigma$-locally Lipschitzian convex processes.''