  A long-standing problem with the many-body approximations for interacting
condensed bosons has been the dichotomy between the ``conserving'' and
``gapless'' approximations, which either obey the conservations laws or satisfy
the Hugenholtz-Pines condition for a gapless excitation spectrum, in the order.
It is here shown that such a dichotomy does not exist for a system of composite
bosons, which form as bound-fermion pairs in the strong-coupling limit of the
fermionic attraction. By starting from the constituent fermions, for which
conserving approximations can be constructed for any value of the mutual
attraction according to the Baym-Kadanoff prescriptions, it is shown that these
approximations also result in a gapless excitation spectrum for the boson-like
propagators in the broken-symmetry phase. This holds provided the corresponding
equations for the fermionic single- and two-particle Green's functions are
solved self-consistently.
