We present a measurement of semi-inclusive spin asymmetries for positively and negatively charged hadrons from deep inelastic scattering of polarised muons on polarised protons and deuterons in the range 0.003 <x <0.7 and Q2 > 1 GeV2. Compared to our previous publication on this subject, with the new data the statistical errors have been reduced by nearly a factor of two. From these asymmetries and our inclusive spin asymmetries we determine the polarised quark distributions of valence quarks and non-strange sea quarks at Q2 = 10 GeV2. The polarised u valence quark distribution, Δuυ(×), is positive and the polarisation increases with x. The polarised d valence quark distribution, Δdυ(x), is negative and the non-strange sea distribution, Δq-(x), is consistent with zero over the measured range of x. We find for the first moments (latin small letter esh)10Δuυ(x)d x = 0.77 ± 0.10 ± 0.08, (latin small letter esh)10Δdυ(x)d x = -0.52 ± 0.14 ± 0.09 and (latin small letter esh)10Δq-(x)d x = 0.01 ± 0.04 ± 0.03, where we assumed Δu-(x) = Δd-(x). We also determine for the first time the second moments of the valence distributions (latin small letter esh)10xΔqυ(x)d x. © 1998 Published by Elsevier Science B.V.