$  u_t= \Delta u + f(x,u),     t>0,   x  \in \Omega,  $

under   Dirichlet boundary condition.  The domain $\Omega$ is assumed
bounded and having smooth boundary. We  prove  that generically with
respect  to $f$  the dynamical system  generated  by this  equation is
Morse-Smale, that is, all  equilibria are hyperbolic and their  stable
and unstable manifolds  intersect transversally.

A significant portion  of the paper is  devoted to abstract  parabolic
equations.  We develop a general scheme for the proof of genericity of
the   Morse-Smale property which   is    based on application of   the
parametric transversality  theorem to  a nonlinear parabolic operator.
Following   the  abstract  scheme,    the genericity   for  the  above
reaction-diffusion equations  proved.  Nodal properties  of  solutions
play a significant role in this proof.