  We estimate the running coupling constant of the strong interactions within
the nonperturbative framework of lattice QCD in Landau gauge. Our calculation
is based on the ghost-gluon vertex which in the particular case of Landau gauge
allows for a definition of alpha(s) in a MOM scheme solely in terms of the
gluon and ghost dressing functions. As a first step we investigate the zero and
two-flavour case and report here on preliminary results.
