  We study the condensate dynamics of the so-called entangled Bose-Einstein
condensation (EBEC), which is the ground state of a mixture of two species of
pseudospin-$\frac{1}{2}$ atoms with interspecies spin-exchange scattering in
certain parameter regimes. EBEC leads to four inter-dependent superfluid
components, each corresponding to the orbital wave function associated with a
spin component of a species. The four superflows have various
counter-relations, and altogether lead to a conserved total supercurrent and a
conserved total spin supercurrent. In the homogenous case, we also obtain the
elementary excitations due to variations of the single-particle orbital wave
functions, by exactly solving the generalized time-dependent Bogoliubov
equations. There are three gapless Bogoliubov modes and one Klein-Gordon-like
gapped mode. The origin of these excitations are also discussed from the
perspective of spontaneous breaking of the symmetries possessed by the system.
