Considering the interspecies and intraspecies interactions as being repulsive, we study the dynamic behaviors of the gray-gray and black-black solitons in two-species Bose-Einstein condensates trapped in the harmonic external potentials. The results show that in the absence of the axial trapping frequencies, both the gray-gray and black-black solitons can keep localization stable. In the presence of the axial trapping frequencies, the gray-gray can be converted into bright-bright solitons.