The author considers successively: 1--The theoretical justifications for horizontal partial laryngectomy (anatomical considerations, indications as to the modalities of extension of supraglottic tumors, results concerning the cancer itself, functional results). 2--The indications of and contraindications for this type of surgery, with special reference to two types of cancers: median supraglottic carcinomas and antero-lateral epilarynx carcinomas. 3--Some specific problems, namely that of large supraglottic laryngectomy, of combined nodal surgery, and of preoperative radiotherapy. The limits of horizontal partial laryngectomy are specified on the basis of two criteria: its value as far as cancer is concerned (five-year survival rate), the quality of functional results.