We study minimal surfaces in sub-Riemannian manifolds with sub -

Riemannian structures of co-rank one. These surfaces can be defined

as the critical points of the so-called horizontal area functional

associated with the canonical horizontal area form. We derive the

intrinsic equation in the general case and then consider in greater

detail 2-dimensional surfaces in contact manifolds of dimension 3. We

show that in this case minimal surfaces are projections of a special

class of 2-dimensional surfaces in the horizontal spherical bundle

over the base manifold. The singularities of minimal surfaces turn out

to be the singularities of this projection, and we give a complete

local classification of them. We illustrate our results by examples in

the Heisenberg group and the group of roto-translations.