We show that in one-dimensional hybrid simulations supercritical perpendicular shocks have a well-defined, slightly oscillating structure (including foot, ramp, overshoot, and undershoot) for hot upstream protons and low Mach numbers. In this case the reflected protons are able to stop the shock steepening at proton scales. However, for colder upstream protons and/or higher Mach numbers simulated shocks show a nonstationary feature, namely a periodic reappearance of a new shock front. These nonstationary shocks simulated by one-dimensional hybrid code have shock front gradient scales that are governed only by the spatial resolution used in the code. Consequently, we conclude that the one-dimensional hybrid code is not suitable for description of perpendicular nonstationary shocks.