The cubic (CsCl-type structure) compounds HoCu, ErCu and TmCu have been investigated by means of specific heat and neutron diffraction experiments. In the three compounds, there exists a competition between various multi- q antiferromagnetic structures (modulated, multiaxis, or simple collinear). At low temperature, they order within the (Π, Π, 0)-type structure. In ErCu and TmCu, this structure is replaced, near the Néel temperature, by a more complex one, which results from the superimposition of the preceding one and of an amplitude-modulated structure; the incommensurate propagation vector is q mod = ( 1 2 ± τ, 1 2 , 0) 2Π a with τ = 0.04 ( ErCu) and 0.06 (TmCu). The situation is different HoCu where two changes in the magnetic moment direction successively occur between the [111] and [101] directions. A first analysis of these peculiar magnetic behaviours is given starting from the crystalline electric-field level scheme and may indicate the possible existence of exchange interactions other than the isotropic bilinear ones.