The evolution of the crystal structure and some magnetic properties of the heavy-fermion material CeCu(6-x)Sn(x) (x = 0, 0.25, 0.65, 0.75, 0.85 and 1.0) has been studied by powder neutron diffraction and by specific heat measurements. The substitution of Cu by Sn suppresses the temperature induced orthorhombic to monoclinic transition, known to occur in the pure CeCu(6) phase. No structural phase transition has been observed in these samples as a function of x but the cell volume increases considerably in an anisotropic way. Sn occupies preferentially the special Cu crystallographic site which is next to each of the four Ce atoms in the unit cell. The transition to antiferromagnetic order, characterizing the samples with higher x, is sensitive to both x and magnetic field. The results are discussed in the context of the competition between Kondo and RKKY interactions in disordered or not heavy-fermion systems and reveal an interesting interplay between composition, structure and magnetism in CeCu(6-x)Sn(x).