Fishes with internalized and endothermic red muscles (i.e. tunas and lamnid sharks) are known for a stiff-bodied form of undulatory swimming, based on unique muscle-tendon architecture that limits lateral undulation to the tail region even though the red muscle is shifted anteriorly. A strong convergence between lamnid sharks and tunas in these features suggests that thunniform swimming might be evolutionarily tied to this specialization of red muscle, but recent observations on the common thresher shark (Alopias vulpinus) do not support this view. Here, we review the fundamental features of the locomotor systems in lamnids and tunas, and present data on in vivo muscle function and swimming mechanics in thresher sharks. These results suggest that the presence of endothermic and internalized red muscles alone in a fish does not predict or constrain the swimming mode to be thunniform and, indeed, that the benefits of this type of muscle may vary greatly as a consequence of body size.