We describe the first experiments that study in a controlled way the d
ynamics of distinguishable and interpenetrating bosonic quantum fluids
. We work with a two-component system of Bose-Einstein condensates in
the \F = 1, m(f) = -1> and \2, 1> spin states of Rb-87. The two conden
sates are created with complete spatial overlap, and in subsequent evo
lution they undergo complex relative motions that tend to preserve the
total density profile. The motions quickly damp out, leaving the cond
ensates in a steady state with a non-negligible (and adjustable) overl
ap region.