Universal pipe connection system comprising: a fitting element comprising a tubular body with an annular bulge at least at an end portion which annular bulge forms on the inner side of the tubular body an annular groove housing a sealing gasket which groove is open towards the inside of the tubular body and which end portion extends on the side opposite to the end of the fitting element by a cylindrical portion, said tubular body forming a fitting socket for the end portion of a pipe; there being provided at least two types of pressing tool having at least two opposite pressing jaws which are intended to cooperate with said end portion (101, 301, 401) of the fitting element, by surrounding it along its circumference and they have a profile of the surface in contact with said end portion shaped such to press said end portion against the end of the pipe inserted into said fitting element, determining in at least one circumferential band adjacent to the bulge a contemporaneous deformation of the wall of the pipe and at least of one cylindrical portion (301, 401) of said end portion (101, 301, 401) that are mechanically clamped together in the circumferential and axial direction and a deformation of the annular bulge that presses the gasket generating the tight sealing effect between said tubular body and the end of the pipe inserted therein, the jaws of one of the at least two types of the said pressing tool having a profile corresponding to a M profile and the other of the said pressing tools having jaws having a profile corresponding to a V profile, wherein the annular bulge and the corresponding annular groove are provided at a given axial distance from the end of the end portion of the tubular body, there being provided an initial cylindrical portion between said end and the side of the bulge facing it; wherein the annular bulge and the corresponding groove have such a geometry and size to cooperate alternatively with two different types of pressing tools selected among the pressing tool of the type having M profile and the pressing tool of the type having V profile; and wherein the system comprises in combination both the pressing tool with jaws having a profile corresponding to the M profile and the pressing tool with jaws having a profile corresponding to the V profile. a fitting element comprising a tubular body with an annular bulge at least at an end portion which annular bulge forms on the inner side of the tubular body an annular groove housing a sealing gasket which groove is open towards the inside of the tubular body and which end portion extends on the side opposite to the end of the fitting element by a cylindrical portion, said tubular body forming a fitting socket for the end portion of a pipe; there being provided at least two types of pressing tool having at least two opposite pressing jaws which are intended to cooperate with said end portion (101, 301, 401) of the fitting element, by surrounding it along its circumference and they have a profile of the surface in contact with said end portion shaped such to press said end portion against the end of the pipe inserted into said fitting element, determining in at least one circumferential band adjacent to the bulge a contemporaneous deformation of the wall of the pipe and at least of one cylindrical portion (301, 401) of said end portion (101, 301, 401) that are mechanically clamped together in the circumferential and axial direction and a deformation of the annular bulge that presses the gasket generating the tight sealing effect between said tubular body and the end of the pipe inserted therein, the jaws of one of the at least two types of the said pressing tool having a profile corresponding to a M profile and the other of the said pressing tools having jaws having a profile corresponding to a V profile, wherein the annular bulge and the corresponding annular groove are provided at a given axial distance from the end of the end portion of the tubular body, there being provided an initial cylindrical portion between said end and the side of the bulge facing it; wherein the annular bulge and the corresponding groove have such a geometry and size to cooperate alternatively with two different types of pressing tools selected among the pressing tool of the type having M profile and the pressing tool of the type having V profile; and wherein the system comprises in combination both the pressing tool with jaws having a profile corresponding to the M profile and the pressing tool with jaws having a profile corresponding to the V profile.