  In this paper we study contact nonholonomic mechanical sys\-tems. We
construct a general framework for non-holonomic constraints in contact geometry
and, in this framework, we define different nonholonomic brackets using
con\-venient \linebreak decompositions of the tangent bundle of the phase
space. \linebreak Furthermore, we prove that all of them coincide. In
particular, one the brackets is a natural extension of that defined by R.J.
Eden, but now it is an almost Jacobi bracket since it is not satisfy the
Leibniz rule.
