Pulse detonation combustors of valveless construction. One valveless pulse detonation combustor, having a tube with a closed end and an open end, is constructed with a flame accelerator within the tube, adjacent the open end. A valveless, apertured flow restrictor is positioned between the flame accelerator and the closed end of the tube. A sparking device is positioned within the tube, between the flow restrictor and the flame accelerator. Valveless fuel and air ports are positioned between the flow restrictor and the closed end of the tube. Substantially right-angle manifold passageways are in communication with each of the ports.