ABSTRACT We report the first hard X-ray observations with NuSTAR of the BL Lac-type blazar PKS 2155-304, augmented with soft X-ray data from XMM-Newton and γ-ray data from the Fermi Large Area Telescope, obtained in 2013 April when the source was in a very low flux state. A joint NuSTAR and XMM spectrum, covering the energy range 0.5-60 keV, is best described by a model consisting of a log-parabola component with curvature and a (local) photon index 3.04 0.15 at photon energy of 2 keV, and a hard power-law tail with photon index 2.2 0.4. The hard X-ray tail can be smoothly joined to the quasi-simultaneous γ-ray spectrum by a synchrotron self-Compton component produced by an electron distribution with index p = 2.2. Assuming that the power-law electron distribution extends down to γmin = 1 and that there is one proton per electron, an unrealistically high total jet power of Lp ∼ 1047 erg s−1 is inferred. This can be reduced by two orders of magnitude either by considering a significant presence of electron-positron pairs with lepton-to-proton ratio , or by introducing an additional, low-energy break in the electron energy distribution at the electron Lorentz factor γbr1 ∼ 100. In either case, the jet composition is expected to be strongly matter-dominated.