We report the growth behaviour of InP, InGaAs and InGaAsP on non-planar InP substrates where ridges were formed with (111)A, (211)A, (111)B and (551BAR) sidewall planes. All three materials grow uniformly on the whole patterned surface with (111)A and (211)A sidewall planes. They grow separately on the plateau and in the valley for the other two structures. The growth front of the InGaAs films is always rippled near the sidewalls, indicating large deviations from lattice-matched composition in these areas, while the growth front in the case of the InP and InGaAsP films remains smooth. Single-step growth of buried double heterostructures with a 1 mum wide rib is realized for the structures with both (111)B and (551BAR) sidewall planes. The growth mechanisms responsible for the observed features are discussed.