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.