  We show theoretically the existence of a metastable state and the possibility
of decay to the ground state through macroscopic quantum tunneling in
two-component Bose-Einstein condensates with repulsive interactions. Numerical
analysis of the coupled Gross-Pitaevskii equations clarifies the metastable
states whose configuration preserves or breaks the symmetry of the trapping
potential, depending on the interspecies interaction and the particle number.
We calculate the tunneling decay rate of the metastable state by using the
collective coordinate method under the WKB approximation. Then the height of
the energy barrier is estimated by the saddle point solution. It is found that
macroscopic quantum tunneling is observable in a wide range of particle
numbers. Macroscopic quantum coherence between two distinct states is
discussed; this might give an additional coherent property of two-component
Bose condensed systems. Thermal effects on the decay rate are estimated.
