The production rates of the orbitally excited mesons, Ds1± and , are measured with the 4.1 million hadronic Z decays recorded by the ALEPH detector during 1991–1995. The mesons are reconstructed in the decay modes , and . The production rate of the Ds1± is measured to be f(Z→Ds1±)=(0.52±0.09±0.06)%, under the assumption that the two considered decay modes of the Ds1± saturate the branching ratio. The production rate of the is determined to be , assuming that the branching fraction of the decay is 45%. The production rates in and decays are measured separately.