An intra-oral mandibular advancement appliance to be inserted in the mouth of a patient so as to maintain an open airway to the patient's throat and thereby improve breathing during sleep. The mandibular advancement appliance has particular application for use by those wishing to reduce the effects of snoring and/or sleep apnea. The appliance includes an upper tray assembly against which is seated the patient's teeth carried by his upper jaw and a lower tray assembly against which the patient's teeth carried by his lower jaw are seated. The lower tray assembly is mated to and slidably adjustable by the patient relative to the upper tray assembly. By virtue of the foregoing, the position of the patient's lower jaw can be selectively and continuously moved forward with respect to the position of the upper jaw to prevent an occlusion of the airway as the patient's condition changes over time.