Ultrasonic surgical devices are increasingly used in oral, craniofacial and maxillofacial surgery to cut mineralized tissue, offering the surgeon high accuracy with minimal risk to nerve and vessel tissue. Power ultrasonic devices operate in resonance, requiring their length to be a half-wavelength or multiple-half-wavelength. For bone surgery, devices based on a half-wavelength have seen considerable success, but longer multiple-half-wavelength endoscopic devices have recently been proposed to widen the range of surgeries. To provide context for these developments, some examples of surgical procedures and the associated designs of ultrasonic cutting tips are presented. However, multiple-half-wavelength components, typical of endoscopic devices, have greater potential to exhibit nonlinear dynamic behaviours that have a highly detrimental effect on device performance. Through experimental characterization of the dynamic behaviour of endoscopic devices, it is demonstrated how geometrical features influence nonlinear dynamic responses. Period doubling, a known route to chaotic behaviour, is shown to be significantly influenced by the cutting tip shape, whereas the cutting tip has only a limited effect on Duffing-like responses, particularly the shape of the hysteresis curve, which is important for device stability. These findings underpin design, aiming to pave the way for a new generation of ultrasonic endoscopic surgical devices.