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, the supporting body being traversed axially by said passage; and - at least one compressible element (12, 18) that is designed to be in contact with said fluid and is configured for compensating possible variations of volume thereof, the at least one compressible element (12, 18) having an axial through cavity; wherein said at least one compressible element (12, 18) is positioned at least in part within said cavity and/or in a stretch of the passage of said supporting body close to said cavity, wherein a first compressible element is positioned at least in part in a stretch of said passage of said supporting body, such that the axial cavity thereof forms a first stretch of said duct, characterized in that - the connection structure comprises a second compressible element positioned on top of said supporting body such that the axial through cavity thereof forms a second stretch of said duct; - between said first compressible element and said second compressible element there extends a part of said supporting body including a respective stretch of said passage, that forms a third stretch of said duct which is intermediate to said first stretch and said second stretch. - 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, the supporting body being traversed axially by said passage; and - at least one compressible element (12, 18) that is designed to be in contact with said fluid and is configured for compensating possible variations of volume thereof, the at least one compressible element (12, 18) having an axial through cavity; - a supporting body of the pressure-sensitive component, defining at least one respective passage, the supporting body being traversed axially by said passage; and - at least one compressible element (12, 18) that is designed to be in contact with said fluid and is configured for compensating possible variations of volume thereof, the at least one compressible element (12, 18) having an axial through cavity; - the connection structure comprises a second compressible element positioned on top of said supporting body such that the axial through cavity thereof forms a second stretch of said duct; - between said first compressible element and said second compressible element there extends a part of said supporting body including a respective stretch of said passage, that forms a third stretch of said duct which is intermediate to said first stretch and said second stretch.