  We introduce the secondary Stiefel-Whitney class $\tilde w_2$ of
homotopically trivial diffeomorphisms and show that a homotopically trivial
symplectomorphism of a ruled 4-manifold is isotopic to identity if and only if
the class $\tilde w_2$ vanishes.
  Using this, we give a detailed description of the combinatorial structure of
the diffeotopy group of ruled symplectic 4-manifolds $X$, either minimal or
blown-up, and its action on the homology and homotopy groups $H_2(X,\zz)$,
$\pi_1(X)$, and $\pi_2(X)$.
