We present theoretical studies of a two-species Bose condensate. Using a new numerical method, we have calculated ground state wave functions and show that, due to interspecies interactions, the condensate mixture displays novel behavior not found in a pure condensate. We compared our results with those of the Thomas-Fermi approximation (TFA) and find that under a broad range of conditions the TFA can be reliably used to predict many qualitative features of the condensates. Using our technique, we have modeled a recent JILA experiment on dual spin-state 87 Rb condensate. Finally, collective excitations of double condensates are discussed.