Reconstructing the chronology of mammalian evolution is a debated issue between molecule- and fossil-based inferences. A methodological limitation of molecules is the evolutionary rate variation among lineages, precluding the application of the global molecular clock. We considered 2422 first and second codon positions of the combined ADRA2B, IRBP, and vWF nuclear genes for a well-documented set of placentals including an extensive sampling of rodents. Using seven independent calibration points and a maximum-likelihood framework, we evaluated whether molecular and paleontological estimates of mammalian divergence dates may be reconciled by the local molecular clocks approach, allowing local constancy of substitution rates with variations at larger phylogenetic scales. To handle the difficulty of choosing among all possible rate assignments for various lineages, local molecular clocks were based on the results of branch-length and two-cluster tests. Extensive lineage-specific variation of evolutionary rates was detected, even among rodents. Cross-calibrations indicated some incompatibilities between divergence dates based on different paleontological references. To decrease the impact of a single calibration point, estimates derived from independent calibrations displaying only slight reciprocal incompatibility were averaged. The divergence dates inferred for the split between mice and rats (approximately 13-19 Myr) was younger than previously published molecular estimates. The most recent common ancestors of rodents, primates and rodents, boreoeutherians, and placentals were estimated to be, respectively, approximately 60, 70, 75, and 78 Myr old. Global clocks, local clocks, and quartet dating analyses suggested a Late Cretaceous origin of the crown placental clades followed by a Tertiary radiation of some placental orders like rodents.