Heat exchanger for a heat generator for room heating and/or for the production of domestic hot water, in particular of the condensation type, said heat exchanger being a cylindrical geometry heat exchanger and comprises a first sensible portion and a second condensing part, and a partition between a hot chamber of said sensible portion and a cold chamber of said condensing portion of said heat exchanger, said heat exchanger further comprising a by-pass apt to place in direct communication the hot chamber of the sensible portion of said heat exchanger with the cold chamber of the condensing portion of said exchanger, said by-pass: - allowing a portion of the hot combustion fumes generated therein by a burner to be withdrawn from said sensible portion for mixing them with the fumes (F-P), escaping from said condensing portion, cold by the effect of the thermal exchange with said heat exchanger - for said portion of the combustion fumes comprising an inlet section communicating with said sensible portion of said heat exchanger and a discharge section downstream of said condensing portion of said heat exchanger said mixing bringing the combustion fumes escaping from said heat exchanger to a sufficiently high temperature to prevent the condensation thereof in the discharge system to the atmosphere caused by the unavoidable cooling thereof therein characterised in that said by-pass: - consists of a hollow tubular body comprising: - at an end thereof, said inlet section for said portion of the combustion fumes - at the end opposite that of said inlet section, a closed bottom, - said discharge section for said portion of the combustion fumes, said discharge section: - allowing said portion of the combustion fumes to radially escape from said bypass - being obtained on at least one portion of the outer side surface of said tubular body - is installed passing-through said partition between said hot chamber of said sensible portion and said cold chamber of said condensing portion of said heat exchanger. - allowing a portion of the hot combustion fumes generated therein by a burner to be withdrawn from said sensible portion for mixing them with the fumes (F-P), escaping from said condensing portion, cold by the effect of the thermal exchange with said heat exchanger - for said portion of the combustion fumes comprising an inlet section communicating with said sensible portion of said heat exchanger and a discharge section downstream of said condensing portion of said heat exchanger said mixing bringing the combustion fumes escaping from said heat exchanger to a sufficiently high temperature to prevent the condensation thereof in the discharge system to the atmosphere caused by the unavoidable cooling thereof therein characterised in that said by-pass: - consists of a hollow tubular body comprising: - at an end thereof, said inlet section for said portion of the combustion fumes - at the end opposite that of said inlet section, a closed bottom, - said discharge section for said portion of the combustion fumes, said discharge section: - allowing said portion of the combustion fumes to radially escape from said bypass - being obtained on at least one portion of the outer side surface of said tubular body - at an end thereof, said inlet section for said portion of the combustion fumes - at the end opposite that of said inlet section, a closed bottom, - said discharge section for said portion of the combustion fumes, said discharge section: - allowing said portion of the combustion fumes to radially escape from said bypass - being obtained on at least one portion of the outer side surface of said tubular body - allowing said portion of the combustion fumes to radially escape from said bypass - being obtained on at least one portion of the outer side surface of said tubular body - is installed passing-through said partition between said hot chamber of said sensible portion and said cold chamber of said condensing portion of said heat exchanger.