[en] The inclusive production of D^*± mesons in two-photon collisions is measured with the ALEPH detector at e⁺e^- centre-of-mass energies from 183 GeV to 209 GeV. A total of 360 ±27D^*± meson events are observed from an integrated luminosity of 699 pb^-1. Contributions from direct and single-resolved processes are separated using the ratio of the transverse momentum p_t^D*± of the D^*± to the visible invariant mass W_vis of the event. Differential cross sections of D^*± production as functions of p_t^D*± and the pseudorapidity vertical stroke η^D*± vertical stroke are measured in the range 2 GeV/c< p_t^D*±<12 GeV/c and vertical stroke η^D*± vertical stroke <1.5. They are compared to next-to-leading order (NLO) perturbative QCD calculations. The extrapolation of the integrated visible D^*± cross section to the total charm cross section, based on the Pythia Monte Carlo program, yields σ(e⁺e^-→e⁺e^- c anti c) _{leftangle√(s)rightangle=197GeV}=731±74_stat±47_syst±157_extr pb. (orig.)