A pressure-sensor device having: - a component sensitive to pressure, comprising a sensor body (5', 5") with a cavity, an elastically deformable membrane part that closes the cavity at an end thereof, and at least one detection element for detecting a deformation of the membrane part; - a structure (2, 3) for housing or supporting the pressure-sensitive component, having a 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 (5', 5") is mounted in such a way that its membrane part is exposed to 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, formed with one or more elastically deformable or compressible materials, - a sealing and/or supporting element (23; 23'), which is set between the supporting body and the sensor body (5', 5"), to define with them a chamber for collecting the fluid, wherein the elastically deformable body defines at least one external compensation element, configured for compensating any possible variations in volume of the fluid, which is in a position generally facing or close to the membrane part of the sensor body (5', 5") and extends at least in part on the outside of the duct of the supporting body; the pressure-sensor device being characterized in that: - a portion of the membrane part of the sensor body (5', 5") extends in a position between the cavity thereof and the at least one external compensation element, - the sealing and/or supporting element (23; 23') extends, with respect to an upper face of the supporting body, to a greater height than the external compensation element; and - the external compensation element is set at a distance from the membrane part and is positioned in an area circumscribed by the sealing and/or supporting element (23; 23'). - a component sensitive to pressure, comprising a sensor body (5', 5") with a cavity, an elastically deformable membrane part that closes the cavity at an end thereof, and at least one detection element for detecting a deformation of the membrane part; - a structure (2, 3) for housing or supporting the pressure-sensitive component, having a 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 (5', 5") is mounted in such a way that its membrane part is exposed to 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, formed with one or more elastically deformable or compressible materials, - a sealing and/or supporting element (23; 23'), which is set between the supporting body and the sensor body (5', 5"), to define with them a chamber for collecting the fluid, wherein the elastically deformable body defines at least one external compensation element, configured for compensating any possible variations in volume of the fluid, which is in a position generally facing or close to the membrane part of the sensor body (5', 5") and extends at least in part on the outside of the duct of the supporting body; the pressure-sensor device being characterized in that: - a portion of the membrane part of the sensor body (5', 5") extends in a position between the cavity thereof and the at least one external compensation element, - the sealing and/or supporting element (23; 23') extends, with respect to an upper face of the supporting body, to a greater height than the external compensation element; and - the external compensation element is set at a distance from the membrane part and is positioned in an area circumscribed by the sealing and/or supporting element (23; 23'). - a portion of the membrane part of the sensor body (5', 5") extends in a position between the cavity thereof and the at least one external compensation element, - the sealing and/or supporting element (23; 23') extends, with respect to an upper face of the supporting body, to a greater height than the external compensation element; and - the external compensation element is set at a distance from the membrane part and is positioned in an area circumscribed by the sealing and/or supporting element (23; 23').