A pressure-sensor device having: - a component sensitive to pressure, comprising a sensor body, with an elastically deformable membrane part, and at least one detection element for detecting a deformation of the membrane; - a structure (2, 3) for housing or supporting the pressure-sensitive component, having at least one passageway for a fluid the pressure of which is to be detected, the housing or supporting structure (2, 3) comprising a supporting body with respect to which the sensor body is positioned in such a way that its membrane part is exposed to the fluid coming out of the passageway, the supporting body having a hydraulic-connection portion and a duct that extends from the hydraulic-connection portion; - at least one elastically deformable body, made with one or more elastically deformable or compressible materials, comprising at least one compressible compensation element (20, 21), configured for compensating any possible variations in volume of the fluid, wherein said at least one elastically deformable body is overmoulded to the housing or supporting structure (2, 3) or an insert thereof, characterized in that the duct has an intermediate transverse wall and comprises, downstream of the transverse wall, a housing portion of the supporting body, partially housed within which is said one compressible compensation element that extends in part on the outside of the duct or of the supporting body. - a component sensitive to pressure, comprising a sensor body, with an elastically deformable membrane part, and at least one detection element for detecting a deformation of the membrane; - a structure (2, 3) for housing or supporting the pressure-sensitive component, having at least one passageway for a fluid the pressure of which is to be detected, the housing or supporting structure (2, 3) comprising a supporting body with respect to which the sensor body is positioned in such a way that its membrane part is exposed to the fluid coming out of the passageway, the supporting body having a hydraulic-connection portion and a duct that extends from the hydraulic-connection portion; - at least one elastically deformable body, made with one or more elastically deformable or compressible materials, comprising at least one compressible compensation element (20, 21), configured for compensating any possible variations in volume of the fluid, wherein said at least one elastically deformable body is overmoulded to the housing or supporting structure (2, 3) or an insert thereof, characterized in that the duct has an intermediate transverse wall and comprises, downstream of the transverse wall, a housing portion of the supporting body, partially housed within which is said one compressible compensation element that extends in part on the outside of the duct or of the supporting body. wherein said at least one elastically deformable body is overmoulded to the housing or supporting structure (2, 3) or an insert thereof, characterized in that the duct has an intermediate transverse wall and comprises, downstream of the transverse wall, a housing portion of the supporting body, partially housed within which is said one compressible compensation element that extends in part on the outside of the duct or of the supporting body.