Neutron-capture nucleosynthesis during core He burning in massive (ZAMS mass = 50-100 solar mass) mass-losing stars, which are identified with Wolf-Rayet stars, is studied in the framework of recent stellar models based on the Roxburgh criterion for convection and on the latest nuclear data available. The nucleosynthesis is followed with the aid of a full nuclear reaction network incorporating up-to-date Maxwellian-averaged neutron-capture cross sections and new density- and temperature-dependent beta-decay rates. Numerical techniques are developed in order to integrate efficiently the set of coupled differential equations of the network. The resulting stellar core and surface abundances are presented, as well as the composition of the stellar winds ejected during the WC phase. Consideration is given to the implications of these results for the composition of OB associations and of the solar system, for the isotopic anomalies in meteorites and in the galactic cosmic rays, as well as for nuclear gamma-ray line astronomy. 114 references.