The alloy contains, by weight, at least 95% zirconium and from 0.01 to 0.1% sulphur and, optionally, at least one element from the group consisting of the elements tin, iron, chromium, hafnium, niobium, nickel, oxygen and vanadium, the balance of the alloy consisting of inevitable impurities. The sulphur is present in the alloy in the dissolved state, thereby improving the creep strength and in the form of uniformly distributed fine precipitates, thereby improving the corrosion and hydriding resistance. The alloy may be heated by a solution annealing treatment in the .beta. phase followed by a quench or by a soak at a temperature below 950.degree. C. in order to transform it into the .alpha. or .alpha.+.beta. phase.