  We consider the post-Newtonian limit of a general class of bimetric theories
of gravity, in which both metrics are dynamical. The established parameterised
post-Newtonian approach is followed as closely as possible, although new
potentials are found that do not exist within the standard frame-work. It is
found that these theories can evade solar system tests of post-Newtonian
gravity remarkably well. We show that perturbations about Minkowski space in
these theories contain both massless and massive degrees of freedom, and that
in general there are two different types of massive mode, each with a different
mass parameter. If both of these masses are sufficiently large then the
predictions of the most general class of theories we consider are
indistinguishable from those of general relativity, up to post-Newtonian order
in a weak field, low velocity expansion. In the limit that the massive modes
become massless, we find that these general theories do not exhibit a van
Dam-Veltman-Zakharov-like discontinuity in their gamma parameter, although
there are discontinuities in other post-Newtonian parameters as the massless
limit is approached. This smooth behaviour in gamma is due to the
discontinuities from each of the two different massive modes cancelling each
other out. Such cancellations cannot occur in special cases with only one
massive mode, such as the Isham-Salam-Strathdee theory.
