Over the (1,N)-dimensional real superspace, N≧3\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$${N \geqq 3}$$\end{document}, we study non-trivial deformations of the natural action of the orthosymplectic Lie superalgebra osp(N|2)\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$${\mathfrak{osp}(N|2)}$$\end{document} 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 K(N)\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$${\mathcal{K}(N)}$$\end{document} of contact vector fields instead of osp(N|2)\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$${\mathfrak{osp}(N|2)}$$\end{document} 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].
