Using data from primates, we show that molecular clocks in sites that have been part of a CpG dinucleotide in recent past (CpG sites) and non-CpG sites are of markedly different nature, reflecting differences in their molecular origins. Notably, single nucleotide substitutions at non-CpG sites show clear generation-time dependency, indicating that most of these substitutions occur by errors during DNA replication. On the other hand, substitutions at CpG sites occur relatively constantly over time, as expected from their primary origin due to methylation. Therefore, molecular clocks are heterogeneous even within a genome. Furthermore, we propose that varying frequencies of CpG dinucleotides in different genomic regions may have contributed significantly to conflicting earlier results on rate constancy of mammalian molecular clock. Our conclusion that different regions of genomes follow different molecular clocks should be considered when inferring divergence times using molecular data and in phylogenetic analysis.