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With the advent of wide-field cosmological surveys, we are approachingsamples of hundreds of thousands of galaxy clusters. While such large numberswill help reduce statistical uncertainties, the control of systematics incluster masses becomes ever more crucial. Here we examine the effects of animportant source of systematic uncertainty in galaxy-based cluster massestimation techniques: the presence of significant dynamical substructure.Dynamical substructure manifests as dynamically distinct subgroups inphase-space, indicating an 'unrelaxed' state. This issue affects around aquarter of clusters in a generally selected sample. We employ a set of mockclusters whose masses have been measured homogeneously with commonly-usedgalaxy-based mass estimation techniques (kinematic, richness, caustic, radialmethods). We use these to study how the relation between observationallyestimated and true cluster mass depends on the presence of substructure, asidentified by various popular diagnostics. We find that the scatter for anensemble of clusters does not increase dramatically for clusters with dynamicalsubstructure. However, we find a systematic bias for all methods, such thatclusters with significant substructure have higher measured masses than theirrelaxed counterparts. This bias depends on cluster mass: the most massiveclusters are largely unaffected by the presence of significant substructure,but masses are significantly overestimated for lower mass clusters, by$\sim10\%$ at $10^{14}$ and $\geq20\%$ for $\leq10^{13.5}$. The use of clustersamples with different levels of substructure can, therefore, bias certaincosmological parameters up to a level comparable to the typical uncertaintiesin current cosmological studies.

Galaxy Cluster Mass Reconstruction Project: III. The impact of dynamical substructure on cluster mass estimates