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 Q(2) > 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 Q(2) = 10 GeV2. The polarised u valence quark distribution, Delta u(v)(x), is positive and the polarisation increases with x. The polarised d valence quark distribution, Delta d(v)(x), is negative and the non-strange sea distribution, Delta (q) over bar(x), is consistent with zero over the measured range of x. We find for the first moments integral(0)(1) Delta u(v)(x)d x = 0.77 +/- 0.10 +/- 0.08, integral(0)(1) Delta d(v)(x)d x = -0.52 +/- 0.14 +/- 0.09 and integral(0)(1) Delta (q) over bar(x)d x = 0.01 +/- 0.04 +/- 0.03, where we assumed Delta (u) over bar(x) = Delta (d) over bar(x). We also determine for the first time the second moments of the valence distributions integral(0)(1)x Delta q(v)(x)d x. (C) 1998 Published by Elsevier Science B.V.