The mechanism for the activation of the a bonds, the O-H of H2O, C-H of CH4, and the H-H of H-2, and the pi bonds, the CdropC of C2H2, C=C of C2H4, and the C=O of HCHO, at the Pd=X (X = Sn, Si, C) bonds of the model complexes (H2PC2H4PH2)Pd=XH2 5 has been theoretically investigated using a density functional method (B3LYP). The reaction is significantly affected by the electronic nature of the Pd=X bond, and the mechanism is changed depending on the atom X. The activation of the O-H bond with the lone pair electron is heterolytic at the Pd=X (X = Sn, Si) bonds, while it is homolytic at the Pd=C bond. The C-H and H-H bonds without the lone pair electron are also heterolytically activated at the Pd=X bonds independent of the atom X, where the hydrogen is extracted as a proton by the Pd atom in the case of X = Sn, Si and by the C atom in the case of X=C because the nucleophile is switched between the Pd and X atoms depending on the atom X. In contrast, the pi bond activation of CdropC and C=C at the Pd=Sn bond proceeds homolytically, and is accompanied by the rotation of the (H2PC2H2PH2)Pd group around the Pd-Sn axis to successfully complete the reaction by both the electron donation from the pi orbital to Sn p orbital and the back-donation from the Pd dpi orbital to the pi* orbital. On the other hand, the activation of the C=O pi bond with the lone pair electron at the Pd=Sn bond has two reaction pathways: one is homolytic with the rotation of the (H2PC2H4PH2)Pd group and the other is heterolytic without the rotation. The role of the ligands controlling the activation mechanism, which is heterolytic or homolytic, is discussed.