In this paper we determine the general family of almost r-paracontact connections on a manifold M and give the conditions for an almost r-paracontact connection to be symmetric. Moreover, we deal with curvature tensors of such connections. 1. An almost r-paracontact connection on a manifold M DEFINITION 1.1 [1]. type (1, 1), r vector fields (1.1) (1.2) (1.3) (1.4)If, on a manifold M, there exist a tensor field ~0 of the r --., 4, and r 1-forms 71 ~, ..., q" such thatwhere the summation convention is employed on repeated indices, then the structure Z=((p, r i=1, ...,r is said to be an almost r-paracontact structure on M.If, moreover, there exists a positive definite Riemannian metric g on M, such that:(1.5) qi(X)=g(X, r i= 1 ..... r, for any vector field X, (1.6) g(~oX, ~oY)=g(X, Y)-~ ~(X)tf(Y) for any vector fields X, Y then S =(q~, ~(~), t/(0, g) i= t, ..., r is called an almost r-paracontact metric structure on M. The metric g is called compatible Riemannian metric.DEFINITION 1.2. Suppose that on a manifold M there is given an almost r-paracontact structure 2;=(9, ~(o, t/(0) i=1 ..... r. A linear connection F on a manifold M given by its covariant derivative S is said to be an almost r-paracontact or simply S-connection if and only if (1.7) Vx~ = 0(1.8) Vxtf=0, i-=-1 .... ,r for every vector field X.