Femtosecond to nanosecond dynamics of O(2) rebinding to human WT myoglobin and its mutants, V68F and I107F, have been studied by using transient absorption. The results are compared with NO rebinding. Even though the immediate environment around the heme binding site is changed by the mutations, the picosecond geminate rebinding of oxygen is at most minimally affected. On the other hand, the V68F (E11) mutation causes drastic differences in rebinding on the nanosecond time scale, whereas the effect of the I107F (G8) mutation remains relatively small within our 10-ns time window. Unlike traditional homogeneous kinetics and molecular dynamics collisional simulations, we propose a "bifurcation model" for populations of directed and undirected dynamics on the ultrafast time scale, reflecting the distribution of initial protein conformations. The major mutation effect occurs on the time scale on which global protein conformational change is possible, consistent with transitions between the conformations of directed and undirected population playing a role in the O(2) binding. We discuss the relevance of these findings to the bimolecular function of the protein.