An apparatus and methods for treating sleep apnea and/or snoring are provided. The apparatus includes an appliance sized and structured to be placed in the pharyngeal region of a human or animal. The appliance, when so placed is effective in treating sleep apnea and/or snoring, for example in maintaining openness of an oropharyngeal region of a human or animal during natural sleep. Preferably, the appliance is non-circumferential in form and includes rounded, spaced apart end portions.