Coupled eigenmodes in a two-component Bose-Einstein condensate

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