The effect of the initial gas mixture pressure on curved detonation propagation modes has been extensively investigated in the present study using a stoichiometric ethylene–oxygen mixture in a new experimental facility consisting of a straight channel section joined to a helical channel section. Flame propagation through the helical channel was observed by high-speed CCD camera, and the trajectories of triple points on the detonation waves were obtained using a soot-deposition plate. The results clearly identify three detonation propagation modes, namely, a stabilized propagation mode, critical mode, and non-stabilized propagation mode, that vary according to the ratio of the radius of curvature of the inside wall ri to the normal detonation cell width λ. For the stabilized propagation mode (ri/λ > 27), the detonation velocity at the inner wall in the curved section asymptotically approaches the detonation velocity in the straight section with increasing initial pressure due to competition between the weakening and strengthening effects characteristic of the curved channel geometry. A definite flame shape, which is perpendicular to the inner wall of the channel, is observed. For the critical mode (16 ≤ ri/λ ≤ 27), the shape of the flame front is observed to be more irregular and unstable than that of the stabilized propagation mode. This mode can be considered as a transition zone, where the stabilized propagation mode transits to the non-stabilized propagation mode with decreasing initial pressure. For the non-stabilized propagation mode (ri/λ < 16), two types of periodic detonation propagation behavior are observed. The first is analogous to single-headed spinning detonation in a circular tube, which is observed in an initial pressure range of 5.5–11 kPa. Soot-coated foil records show that the cellular structure has specific features of the periodic variation, such as re-generation, decrease, and partial disappearance of detonation near the inner wall. The angular interval of consecutive cycles for sinning-like detonation decreases with increasing initial pressure. The second is galloping detonation near the detonation propagation limit. In one cycle of galloping detonation, a change from multi-headed to single-headed cellular structure is observed. However, as the galloping detonation further decays to the low velocity phase of the galloping cycle, the cellular structure vanishes. The angular interval of consecutive cycles for galloping detonation is observed to be random. Although both spinning-like and galloping detonations periodically undergo the process of re-generation, decrease, and failure, they exhibit two different propagation behaviors. The former partially fails near the inner wall, and is re-initiated by transverse detonation from the outer wall, while the latter fails completely, and re-generates by local explosion at the outer wall.