A regulating slide valve apparatus having a housing which forms a duct through which a gaseous or liquid medium can flow having an inlet longitudinal portion, an outlet longitudinal portion, and an adjustable regulating element for varying the flow cross section of the duct and adjusting the throughflow rate. A seat ring element is provided in the duct, the regulating element has a first longitudinal portion which has a circular cross section with diameters that vary in the longitudinal direction, and the regulating element is adjustable in the longitudinal direction of the duct along an adjustment travel. In a closure position the regulating element lies against the seat ring element and closes the duct and, in an open position, forms an annular gap through which flow can pass, with the seat ring element. The varying diameters along the first longitudinal portion of the regulating element are configured such that the change in the cross-sectional area through which flow can pass, of the annular gap with the adjustment of the regulating element in the longitudinal direction, is such that the volume flow through the annular gap varies approximately linearly with the adjustment of the regulating element along the adjustment travel.