We present a broad–band ( \sim 0.3–70 keV ) spectral and temporal analysis of NuSTAR observations of the luminous infrared galaxy NGC 6240 , combined with archival Chandra , XMM–Newton and BeppoSAX data . NGC 6240 is a galaxy in a relatively early merger state with two distinct nuclei separated by \sim 1 \aas@@fstack { \prime \prime } 5 . Previous Chandra observations have resolved the two nuclei , showing that they are both active and obscured by Compton–thick material . Although they can not be resolved by NuSTAR , thanks to the unprecedented quality of the NuSTAR data at energies > 10 keV , we clearly detect , for the first time , both the primary and the reflection continuum components . The NuSTAR hard X–ray spectrum is dominated by the primary continuum piercing through an absorbing column density which is mildly optically thick to Compton scattering ( \tau \simeq 1.2 , N _ { H } \sim 1.5 \times 10 ^ { 24 } cm ^ { -2 } ) . We detect moderate hard X–ray ( > 10 keV ) flux variability up to 20 % on short ( 15 - 20 ksec ) timescales . The amplitude of the variability is maximum at \sim 30 keV and is likely to originate from the primary continuum of the southern nucleus . Nevertheless , the mean hard X–ray flux on longer timescales ( years ) is relatively constant . Moreover , the two nuclei remain Compton–thick , although we find evidence of variability of the material along the line of sight with column densities N _ { H } \leq 2 \times 10 ^ { 23 } cm ^ { -2 } over long ( \sim 3–15 years ) timescales . The observed X–ray emission in the NuSTAR energy range is fully consistent with the sum of the best–fit models of the spatially resolved Chandra spectra of the two nuclei .