  We propose a free field representation for the form factors of descendant
operators in the Bullough-Dodd model. This construction is a particular
modification of Lukyanov's technique for solving the form factors axioms. We
prove that the number of proposed solutions in each level subspace of the
chiral sectors coincide with the number of the corresponding descendant
operators in the Lagrangian formalism. We check that these form factors possess
the cluster factorization property. Besides, we propose an alternative free
field representation which allows us to study analytic properties of the form
factors effectively. In particular, we prove that the form factors satisfy non
trivial identities known as the "reflection relations". We show the existence
of the reflection invariant basis in the level subspaces for a generic values
of the parameters.
