A pressure-sensor device that comprises: - a pressure-sensitive component having a body, in particular of a monolithic type, in which a blind cavity is defined with a bottom surface and a peripheral surface, said bottom surface belonging to a membrane portion of said body, to said membrane portion there being operatively associated a detection element; and - a connection structure having a duct in communication with said cavity, that is to receive a fluid, a pressure of which is to be detected, said structure comprising: - a supporting body of the pressure-sensitive component, defining at least one respective passage; and - a first compressible element that is designed to be in contact with said fluid and is configured for compensating possible variations of volume thereof; wherein said first compressible element is positioned at least in part within said cavity, characterized in that - said first compressible element is positioned on top of said supporting body, - the connection structure further comprises a second compressible element positioned in a stretch of the passage of said supporting body close to said cavity, such that between said first compressible element and said second compressible element is a part of said supporting body including a stretch of the corresponding passage, - the first compressible element and the second compressible element are configured in a single piece, - provided between the first compressible element and the second compressible element is an intermediate portion of said single piece, said intermediate portion extending through said part of the supporting body and connecting the two compressible elements (12, 18). - a pressure-sensitive component having a body, in particular of a monolithic type, in which a blind cavity is defined with a bottom surface and a peripheral surface, said bottom surface belonging to a membrane portion of said body, to said membrane portion there being operatively associated a detection element; and - a connection structure having a duct in communication with said cavity, that is to receive a fluid, a pressure of which is to be detected, said structure comprising: - a supporting body of the pressure-sensitive component, defining at least one respective passage; and - a first compressible element that is designed to be in contact with said fluid and is configured for compensating possible variations of volume thereof; - a supporting body of the pressure-sensitive component, defining at least one respective passage; and - a first compressible element that is designed to be in contact with said fluid and is configured for compensating possible variations of volume thereof; - said first compressible element is positioned on top of said supporting body, - the connection structure further comprises a second compressible element positioned in a stretch of the passage of said supporting body close to said cavity, such that between said first compressible element and said second compressible element is a part of said supporting body including a stretch of the corresponding passage, - the first compressible element and the second compressible element are configured in a single piece, - provided between the first compressible element and the second compressible element is an intermediate portion of said single piece, said intermediate portion extending through said part of the supporting body and connecting the two compressible elements (12, 18).