  Single-spin asymmetries have been measured for semi-inclusive
electroproduction of $\pi^+$, $\pi^-$, $\pi^0$ and $K^+$ mesons in
deep-inelastic scattering off a longitudinally polarised deuterium target. The
asymmetries appear in the distribution of the hadrons in the azimuthal angle
$\phi$ around the virtual photon direction, relative to the lepton scattering
plane. The corresponding analysing powers in the $\sin \phi$ moment of the
cross section are $0.012 \pm 0.002 {(stat.)} \pm 0.002 {(syst.)}$ for $\pi^+$,
  $0.006 \pm 0.003 {(stat.)} \pm 0.002 {(syst.)}$ for $\pi^-$,
  $0.021 \pm 0.005 {(stat.)} \pm 0.003 {(syst.)}$ for $\pi^0$ and $0.013 \pm
0.006 {(stat.)} \pm 0.003 {(syst.)}$ for $K^+$. The $\sin 2\phi$ moments are
compatible with zero for all particles.
