Context : The mechanisms giving rise to diffuse radio emission in galaxy clusters , and in particular their connection with cluster mergers , are still debated . Aims : We aim to obtain new insights into the internal dynamics of the cluster Abell 1240 , showing the presence of two roughly symmetric radio relics , separated by \sim 2 h _ { 70 } ^ { -1 } Mpc . Methods : Our analysis is mainly based on redshift data for 145 galaxies mostly acquired at the Telescopio Nazionale Galileo and on new photometric data acquired at the Isaac Newton Telescope . We also use X–ray data from the Chandra archive and photometric data from the Sloan Digital Sky Survey ( Data Release 7 ) . We combine galaxy velocities and positions to select 89 cluster galaxies and analyze the internal dynamics of the Abell 1237 + Abell 1240 cluster complex , being Abell 1237 a close companion of Abell 1240 towards the southern direction . Results : We estimate similar redshifts for Abell 1237 and Abell 1240 , \left < z \right > = 0.1935 and \left < z \right > = 0.1948 , respectively . For Abell 1237 we estimate a line–of–sight ( LOS ) velocity dispersion \sigma _ { V } \sim 740 km s ^ { -1 } and a mass M \sim 6 \times 10 ^ { 14 } h _ { 70 } ^ { -1 } M _ { \odot } . For Abell 1240 we estimate a LOS \sigma _ { V } \sim 870 km s ^ { -1 } and a mass range M \sim 0.9 - 1.9 \times 10 ^ { 15 } h _ { 70 } ^ { -1 } M _ { \odot } , which takes into account its complex dynamics . Abell 1240 is shown to have a bimodal structure with two galaxy clumps roughly defining the N–S direction , the same one defined by the elongation of its X–ray surface brightness and by the axis of symmetry of the relics . The two brightest galaxies of Abell 1240 , associated to the northern and southern clumps , are separated by a LOS rest–frame velocity difference V _ { rf } \sim 400 km s ^ { -1 } and by a projected distance D \sim 1.2 h _ { 70 } ^ { -1 } Mpc . The two–body model agrees with the hypothesis that we are looking at a cluster merger occurred largely in the plane of the sky , with the two galaxy clumps separated by a rest–frame velocity difference V _ { rf } \sim 2000 km s ^ { -1 } at a time of 0.3 Gyrs after the crossing core , while Abell 1237 is still infalling onto Abell 1240 . Chandra archive data confirm the complex structure of Abell 1240 and allow us to estimate a global X–ray temperature T _ { X } = 6.0 \pm 0.5 keV . Conclusions : In agreement with the findings from radio data , our results for Abell 1240 strongly support the “ outgoing merger shocks ” model to explain the presence of the relics .