Abstract
Over the (1,N)-dimensional real superspace, , we study non-trivial deformations of the natural action of the orthosymplectic Lie superalgebra on the direct sum of the superspaces of weighted densities. We compute the necessary and sufficient integrability conditions of a given infinitesimal deformation of this action and prove that any formal deformation is equivalent to its infinitisemal part. Likewise we study the same problem for the Lie superalgebra of contact vector fields instead of getting the same results. This work is the simplest generalization of a result by I. Basdouri and M. Ben Ammar [4] and F. Ammar and K. Kammoun [3].