  Let M be a smooth manifold, A a local algebra in sense of Andr\'e Weil, M^{A}
the manifold of near points on M of kind A and X(M^{A}) the module of vector
fields on M^{A}. We give a new definition of vector fields on M^{A} and we show
that X(M^{A}) is a Lie algebra over A. We study the cohomology of
A-differential forms.
