Using a full-potential \textit{ab-initio} technique I study the electronic and magnetic properties of the (001) surfaces of the half-Heusler alloys, NiMnSb, CoMnSb and PtMnSb and of the full-Heusler alloys Co$_2$MnGe, Co$_2$MnSi and Co$_2$CrAl. The MnSb terminated surfaces of the half-Heusler compounds present properties similar to the bulk compounds and, although the half-metallicity is lost, an important spin-polarisation at the Fermi level. In contrast to this the Ni terminated surface shows an almost zero net spin-polarisation. While the bulk Co$_2$MnGe and Co$_2$MnSi are almost half-ferromagnetic, their surfaces lose the half-metallic character and the net spin-polarisation at the Fermi level is close to zero. Contrary to these compounds the CrAl terminated (001) surface of Co$_2$CrAl shows a spin polarisation of about 84%. Comment: 14 pages, 6 figures