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Rate variation adds considerable complexity to divergence time estimation in molecular phylogenies. Here, we evaluate the impact of lineage-specific rates-which we define as among-branch-rate-variation that acts consistently across the entire genome. We compare its impact to residual rates-defined as among-branch-rate-variation that shows a different pattern of rate variation at each sampled locus, and gene-specific rates-defined as variation in the average rate across all branches at each sampled locus. We show that lineage-specific rates lead to erroneous divergence time estimates, regardless of how many loci are sampled. Further, we show that stronger lineage-specific rates lead to increasing error. This contrasts to residual rates and gene-specific rates, where sampling more loci significantly reduces error. If divergence times are inferred in a Bayesian framework, we highlight that error caused by lineage-specific rates significantly reduces the probability that the 95% highest posterior density includes the correct value, and leads to sensitivity to the prior. Use of a more complex rate prior-which has recently been proposed to model rate variation more accurately-does not affect these conclusions. Finally, we show that the scale of lineage-specific rates used in our simulation experiments is comparable to that of an empirical data set for the angiosperm genus Ipomoea. Taken together, our findings demonstrate that lineage-specific rates cause error in divergence time estimates, and that this error is not overcome by analyzing genomic scale multilocus data sets. [Divergence time estimation; error; rate variation.].