Different types of nucleotide substitutions experience different patterns of rate change over time. We propose clustering context-dependent (or context-independent) nucleotide substitution types according to how their rates change and then using the grouping for divergence time estimation. With our models, relative rates among types that are in the same group are fixed, whereas absolute rates of the types within a group change over time according to a shared relaxed molecular clock. We illustrate our procedure by analysing a 0.15 Mb intergenic region to infer divergence times relating eight primates. The different groupings of substitution types that we explore have little effect on the posterior means of divergence times, but the widths of the credibility intervals decrease as the number of groups increases.This article is part of the themed issue 'Dating species divergences using rocks and clocks'.