A ventilator that delivers air at different pressures to a patient during inspiratory and expiratory cycles of breathing and that cycles from inspiratory to expiratory operation when the patient's respiratory flow passes a threshold level. The threshold generally increases from the beginning of inspiration to the end of inspiration. The increase can be linear over all or only a portion of the inspiratory cycle, and the threshold can be adjusted so that cycling is prevented during the initial portion of an inspiratory cycle. The minimum and maximum levels may both be functions of peak flow and the threshold may increase as a function of elapsed inspiratory time. The rate at which the threshold increases from a minimum level to a maximum level may be adjustable for individual patient needs and may be determined from previous breaths.