A control and operating unit for sliding doors or windows, the control and operating unit comprising at least: - a mounting member which can be associated, in use and frontally, with the inside of the edge profile of an upright of the sash, defined by a main groove delimited by two longitudinal walls (5, 6) of the upright of the door or window sash; - a control box associated with the mounting member, equipped with a housing for receiving the shaft of a handle, passing through a part of the upright, and with a kinematic unit which transmits the movement imparted by the handle and which is connected to - an operating rod positioned along and parallel to the mounting member and movable in both directions relative to the selfsame mounting member; the operating rod being provided with at least one closing member protruding from a corresponding slot formed in the mounting member to be engaged, in use, with a striker element located on the front of the upright of the fixed frame of the door or window; - fastening means by which the mounting member is joined to the sash and which are configured to fix the mounting member to the inside of the main groove also by abutment against a pair of opposed flanges (15, 16) protruding transversely from the walls of the upright and defining a secondary, inner channel together with the bottom wall of the main groove; the fastening means by which the mounting member is joined to the upright comprising at least a plug for positioning and centring the mounting member in the main groove, characterized in that the fastening means by which the mounting member is joined to the upright comprise: - a spacer element associated with, and protruding from, the mounting member on the side of it opposite to that from which the closing member protrudes; - the plug for positioning and centring the mounting member in the main groove is configured to be stably coupled to the spacer element before being housed in the main groove; the plug having at least one pair of flexible wings (24, 25) which are configured so that, in use, they can be inserted by elastic deformation into the secondary channel from the front so that at least part of the plug can then be stably housed in the selfsame secondary channel; the plug having a cavity configured to be stably coupled with the spacer element. - a mounting member which can be associated, in use and frontally, with the inside of the edge profile of an upright of the sash, defined by a main groove delimited by two longitudinal walls (5, 6) of the upright of the door or window sash; - a control box associated with the mounting member, equipped with a housing for receiving the shaft of a handle, passing through a part of the upright, and with a kinematic unit which transmits the movement imparted by the handle and which is connected to - an operating rod positioned along and parallel to the mounting member and movable in both directions relative to the selfsame mounting member; the operating rod being provided with at least one closing member protruding from a corresponding slot formed in the mounting member to be engaged, in use, with a striker element located on the front of the upright of the fixed frame of the door or window; - fastening means by which the mounting member is joined to the sash and which are configured to fix the mounting member to the inside of the main groove also by abutment against a pair of opposed flanges (15, 16) protruding transversely from the walls of the upright and defining a secondary, inner channel together with the bottom wall of the main groove; - a spacer element associated with, and protruding from, the mounting member on the side of it opposite to that from which the closing member protrudes; - the plug for positioning and centring the mounting member in the main groove is configured to be stably coupled to the spacer element before being housed in the main groove; the plug having at least one pair of flexible wings (24, 25) which are configured so that, in use, they can be inserted by elastic deformation into the secondary channel from the front so that at least part of the plug can then be stably housed in the selfsame secondary channel; the plug having a cavity configured to be stably coupled with the spacer element.