  In this paper we prove first a general theorem on semiorthogonal
decompositions in derived categories of coherent sheaves for flat families over
a smooth base. Based on the results of math.AG/0510670, we then show that the
derived categories of coherent sheaves on flag varieties of classical type are
generated by complete exceptional collections. Finally, we find complete
exceptional collections in the derived categories of some homogeneous spaces of
the symplectic groups of small rank.
