  We present the analysis of four NuSTAR observations of the luminous infrared
galaxy merger NGC 6240, hosting a close pair of highly obscured active galactic
nuclei (AGN). Over a period of about two years, the source exhibits hard X-ray
variability of the order of 20 per cent, peaking around 20 keV. When the two
AGN are resolved with Chandra, column densities in the range $N_\textrm{H} \sim
1-2 \times 10^{24}$ cm$^{-2}$ are estimated for both of them. The exact values
are hard to determine, as they appear to depend on aspects that are sometimes
overlooked in Compton-thick objects, such as the covering factor of the
absorber, iron abundance, and the contamination in the Fe-K band from
foreground hot-gas emission. Nearly spherical covering and slightly subsolar
iron abundance are preferred in this case. While the southern nucleus is
suggested to be intrinsically more powerful, as also implied by the mid-IR and
2-10 keV brightness ratios, solutions involving a similar X-ray luminosity of
the two AGN cannot be ruled out. The observed variability is rather limited
compared to the one revealed by the Swift/BAT light curve, and it can be fully
explained by changes in the continuum flux from the two AGN, without requiring
significant column density variations. NGC 6240 is hereby confirmed to
represent a unique opportunity to investigate the X-ray (and broad-band)
properties of massive galaxy mergers, which were much more frequent in the
early Universe.
