  We consider a mixture of two species of spin-1 atoms with interspecies spin
exchange, which may cooperate or compete with the intraspecies spin exchanges
and thus dramatically affect the ground state. It represents a new class of
bosonic gases differing from single-species spinor gases. We determine the
exact ground states in several parameter regimes, and study the composite
structures by using the generating function method generalized here to be
applicable to a mixture of two species of spinor gases. The most interesting
phase is the so-called entangled Bose-Einstein condensation (BEC), which is
fragmented BEC with quantum entanglement between the two species, and with both
interspecies and intraspecies singlet pairs. For comparison, we also apply the
generating function method to a mixture of two species of pseudospin-1/2 atoms,
for which the total spin quantum number of each species is fixed as half of the
atom number, in contrast with the case of spin-1, for which it is a variable
determined by energetics. Consequently, singlet pairs in entangled BEC of a
pseudospin-1/2 mixture are all interspecies. Interspecies spin exchange leads
to novel features beyond those of spinor BEC of a single species of atoms as
well as mixtures without interspecies spin exchange.
