Anguilliform mode swimmers pass waves of lateral bending down their elongate bodies to propel forward. Hagfishes (Myxinidae) are classified as anguilliform swimmers, but their unique habits and reduced morphology--including a flexible body lacking a vertebral column--have the potential to translate into unique swimming behaviour within this broad classification. Their roles as active scavengers and hunters can require considerable bouts of swimming, yet quantitative data on hagfish locomotion are limited. Here, we aim to provide a more complete mechanistic understanding of hagfish swimming by quantifying whole-body kinematics of steady swimming in Pacific hagfish (Eptatretus stoutii (Lockington, 1878)) and Atlantic hagfish (Myxine glutinosa L., 1758), species from the two main lineages of Myxinidae. We analyzed high-speed video of hagfishes swimming at voluntary swim speeds and found that both species swim using high-amplitude undulatory waves. Swim speed is generally frequency-modulated, but patterns in wave speed, wavelength, and amplitude along the body and across swim speeds are variable, implying versatile mechanisms for the control of swim speed in these highly flexible fishes. We propose mechanistic explanations for this kinematic variability and compare hagfish with other elongate swimmers, demonstrating that the hagfish's rich locomotory repertoire adds variety to the already diverse set of locomotory kinematics found in anguilhform swimmers.