We report on measurements of the magnetization M, specific heat C, resistivity rho, and magnetoresistivity of CeCu6-xAux single crystals (x=0.3 and 0.5) grown by the Czochralski method. Antiferromagnetic ordering is observed in M and C for temperatures less than T(N)=0.48 K (x=0.3) and 0.95 K (x=0.5), similar to the ordering temperatures found previously for polycrystalline samples. As a function of magnetic field B, M(B) and C(T, B) are strongly anisotropic, with the easy axis along the crystallographic c direction (orthorhombic notation) as for pure CeCu6. For large magnetic fields where the magnetic ordering is suppressed, the specific heat can be described by the resonance-level model suggestive of a single-ion Kondo effect, similar to CeCu6 where for large B the short-range magnetic correlations are suppressed. The averaged Kondo temperature as determined from a number of properties decreases with increasing x, with T(K)=4.0 K for x=0.3 and 3.0 K for x=0.5, compared to 5.8 K for x=0. The magnetoresistivity shows a negative contribution arising from incoherent Kondo scattering and a positive contribution associated with the magnetic order.