The physical properties of the unconventional PuCoGa5 superconductor are analysed in the framework of the d-wave Eliashberg theory, assuming phonon-mediated Cooper pairing. The solutions of the Eliashberg equations in the imaginary axis representation provide a time variation of thecritical temperature in agreementwith experimental findings collected over atime period of almost fiveyears. The real-axis formulation has then been used tocalculate the temperature dependence of a number of observables (quasiparticle density of states, local spin susceptibility, spin–lattice relaxation rate), which compare very favourably with experiments. The normal state resistivity can also be reproduced within a two-band model up to room temperature. Finally, the energy dependence of theCooper-pair quasiparticle density of state at T = 4 K is calculated for several values of the impurity scattering rate.