The RECuAs2-xPx phases undergo symmetry-breaking transitions from tetragonal HfCuSi2-type structures (P4/nmm space group) to orthorhombic GdCuAs1.15P0.85-type structures (Pmmn space group) upon substitution of arsenic by phosphorus. According to Landau theory, the distortions correspond to the Big irreducible representation and can be continuous. The P4/nmm --> Pmmn transitions are not caused by a Peierls-like instability of the square As/P nets but result from a structural adaptation for the smaller P atoms. The stability of the tetragonal RECuAs2-xPx and other REMX2 structures with respect to the orthorhombic distortion can be characterized by a relative interatomic distance in the As/P or X layer. Although the tetragonal phases have small relative As/P-As/P or X-X interatomic distances, the orthorhombic phases have larger distances.