Crimping apparatus for crimping pipe fitting members on flexible pipes, comprising: - a crimping unit capable of assuming an open configuration and a closed configuration, and including a pair of relatively movable jaws (40, 42) between which a crimping cavity is defined, which is adapted to receive a pipe (14, 14a) and a respective pipe fitting to be crimped, which crimping cavity, in the open configuration of the crimping unit, is accessible from the outside of the apparatus through a side opening, - a set of crimping teeth facing said cavity, which are movable between an at least partly rearward position with respect to said cavity, and a forward position in which they project radially into the cavity in order to interfere with said pipe fitting to connect it by crimping to said pipe (14, 14a), - means (40, 42, 50, 52, 56, 58) for moving the crimping teeth between said rearward and forward positions, - a stationary structure for positioning at least one pipe (14, 14a) and at least one pipe fitting in a predetermined crimping configuration, and movement means for spatially moving the crimping unit, which are adapted to bring the crimping unit to at least one zone of said at least one pipe (14, 14a) that is positioned on the stationary structure, in order to perform a crimping operation of said at least one pipe fitting on said at least one pipe (14, 14a), characterized in that it comprises a pair of actuating arms (34, 36) each of which is connected to a respective jaw (40, 42) of the crimping unit to cause the movement of the crimping jaws (40, 42) along a common direction of displacement, between a spaced position, in which a pipe (14, 14a) to be crimped can be introduced radially in said crimping cavity together with a respective pipe fitting, and a close position, in which said crimping cavity is radially closed outwards, both said actuating arms (34, 36) having a first end and a second end, the second end of each actuating arm (34, 36) being articulably connected to a respective jaw (40, 42) of the crimping unit by a respective hinge pin, said crimping unit comprising a frame provided with connection means to connect it to said movement means, which frame supports an actuator for controlling the movement of said actuating arms (34, 36), the first end of both said actuating arms (34, 36) being articulated to a common rotation pin which is connected to a portion of said actuator that is movable with respect to said frame, which frame supports linear guide means (44, 46, 48) to guide a sliding movement of said jaws (40, 42) along said common direction of displacement. - a crimping unit capable of assuming an open configuration and a closed configuration, and including a pair of relatively movable jaws (40, 42) between which a crimping cavity is defined, which is adapted to receive a pipe (14, 14a) and a respective pipe fitting to be crimped, which crimping cavity, in the open configuration of the crimping unit, is accessible from the outside of the apparatus through a side opening, - a set of crimping teeth facing said cavity, which are movable between an at least partly rearward position with respect to said cavity, and a forward position in which they project radially into the cavity in order to interfere with said pipe fitting to connect it by crimping to said pipe (14, 14a), - means (40, 42, 50, 52, 56, 58) for moving the crimping teeth between said rearward and forward positions, - a stationary structure for positioning at least one pipe (14, 14a) and at least one pipe fitting in a predetermined crimping configuration, and movement means for spatially moving the crimping unit, which are adapted to bring the crimping unit to at least one zone of said at least one pipe (14, 14a) that is positioned on the stationary structure, in order to perform a crimping operation of said at least one pipe fitting on said at least one pipe (14, 14a),