Specific heatCp, a.c. and d.c. magnetic susceptibility χ, electrical resistivity ρ and upper critical fieldHc 2measurements were performed in two Zr-Ce alloys with 1·3 and 2·3 at.% Ce, whose superconducting transition temperatureTcand Sommerfeld coefficient γ are enhanced with respect to those of pure Zr. In the case of the 2·3 at.% Ce alloy, for whichTc(= 2·85 K) and γ (= 13·4 mJ K−2mol−1) are almost five times larger than those of Zr, the dHc 2/dTslope is - 3·5 T K−1and ρ(T) shows a Kondo-like maximum at 20 K. ItsCp(T) dependence follows a power law (T3) forT< ½Tc, with a jump atTcof ΔCp≈ 1·1 γTc. The superconducting parameters of this sample, extracted fromCp(T) andHc 2, are in better agreement with the prediction for a p-wave-type superconductor (with an axial symmetry order parameter) rather than with those for a conventional Bardeen-Cooper-Schrieffer system.