This presentation gives a current overview of the results obtained in situ and in real time by reflection-anisotropy (RA) spectroscopy, and complemented by RHEED, in the P-capable MBE machine at Sheffield. Recent work dedicated to InP and InAs, as less investigated materials, is examined. Particular emphasis is put on the different phases in the static surface-phase diagrams, as well as the possibility to observe growth oscillations. The low-temperature c(4×4) surface reconstruction on (001)InP displays a RA signature with P-dimers along [11̄0] as opposed to the conventional model derived from the GaAs case. The newly observed by RA spectroscopy γ(2×4) phase in InAs, confirmed by other groups' calculations, appears as the lowest temperature reconstruction observed in this material. The transition towards the less As-rich and higher temperature phase, β(2×4), takes place over a wide temperature region, exhibiting a `solid-solution'-type behaviour between the two phases. Monolayer growth oscillations in the time-resolved RA signal are observed for both InP and InAs. The RA signal shows that upon operating the group-III beam shutter the surface stoichiometry changes much quicker than one monolayer period. This is discussed in conjunction with existing literature on STM of static surfaces, and in the case of InP a model for the sequence of the surface reconstructions during the monolayer growth cycle is suggested.