Sound source localization is an important function in robot audition. The existing works perform sound source localization using static microphone arrays. This work proposes a framework that simultaneously localizes the mobile robot and multiple sound sources using a microphone array on the robot. First, an eigenstructure-based generalized cross correlation method for estimating time delays between microphones under multi-source environments is described. A method to compute the far field source directions as well as the speed of sound using the estimated time delays is proposed. In addition, the correctness of the sound speed estimate is utilized to eliminate spurious sources, which greatly enhances the robustness of sound source detection. The arrival angles of the detected sound sources are used as observations in a bearings-only SLAM procedure. As the source signals are not persistent and there is no identification of the signal content, data association is unknown which is solved using FastSLAM. The experimental results demonstrate theeffectiveness of the proposed approaches.