Measurements of the subjet structure of quark and gluon jets in hadronic Z decays are presented. The analysis is based on one million hadronic events recorded by the ALEPH detector. Roughly symmetric three-jet events are selected with a coarse jet-resolution cut-off, y1. Gluon jets are identified with a purity of 94.6% in those events where evidence of long-lived heavy-flavour hadrons in the other two jets is found. The jets are then analyzed using a smaller cut-off y0 (< y1) so that subjets are resolved. The properties of the jets (subjet multiplicities <Nq>, <Ng> and rates Rg(q)n for n = 1,2,3,4) are determined and are found to be in good agreement with the expectations of perturbative QCD as long as the subjet resolution parametery0 is sufficiently large to keep non-perturbative effects small. In particular, the ratio<Ng - 1>/(<Nq - 1>) , which to leading order in QCD is given by the ratio of colour factors CA/(CF) =9/(4) , is measured to be 1.96 +/- 0.15 for y0 = 2 . 10-3, but falls to 1.29 +/- 0.03 for y0 = 1.6 . 10-5.
