  We have studied the elementary excitations in a two-component Bose-Einstein
condensate. We concentrate on the breathing modes and find the elementary
excitations to possess avoided crossings and regions of coalescing oscillations
where both components of the condensates oscillate with same frequency. For
large repulsive interactions between the condensates, their oscillational modes
tend to decouple due to decreased overlap. A thorough investigation of the
eigenmodes near the avoided crossings is presented.
