The sounding mechanism of a simple clarinetlike system has been investigated experimentally and numerically. The system consists of a cylindrical pipe fitted with the clarinet mouthpiece. By artificial blowing, it produced various periodic and quasiperiodic sounds, among which the lowest pitch was C♯3. In particular, hysteresis of the vibratory state transitions was observed when the flowing pressure was increased and decreased under the same lip adjustment. This was also observed for the artificially blown clarinet. The behavior of the simple system is analyzed numerically by using the Schumacher model [Acustica 48, 71–85 (1981)]. The numerical model is characterized as a double-delayed feedback system represented by a simple reflection function consisting of two separated narrow Gaussian peaks. One of the peaks is due to the main reflection from the open end of the cylindrical air column, and the other, which introduces a short delay, originates from the inside discontinuity of the mouthpiece. This numerical model reproduces well nonlinear vibrations of the clarinetlike system, as well as the hysteretic transition between vibratory states.