Interface states can occur in semiconductor heterojunctions whenever a significant perturbation is present across the interface, for example, interface defects, lattice mismatch, change of sign in the effective mass, or sharp variations in the potential. We discuss here a different type of natural interface states appearing in perfectly coherent and isovalent III--V heterojunctions even in the absence of such extreme perturbations. Using atomistic empirical pseudopotential calculations we find that this is a general phenomenon occurring whenever the junction is formed by two semiconductors having their respective conduction band minima in two different valleys which: (i) fold into the same $\stackrel{P\vec}{q}$ point of the two-dimensional Brillouin zone and (ii) are allowed by symmetry to couple at this point $\stackrel{P\vec}{q}$. In this case, the system manifests two potential wells of opposite attractiveness, such as a well for $\ensuremath{\Gamma}$ states and a barrier for $X$ states. For InP/GaP this leads to the formation of an interface-localized state already in a single heterojunction, lying energetically between the $\ensuremath{\Gamma}$ edge of InP and the $X$ edge of GaP. When the InP/GaP quantum well is formed, this single state evolves into a pair of interface-localized states, located deep in the band gap. Because of their mixed $\ensuremath{\Gamma}\ensuremath{-}X$ character, these interface-localized states possess a strong optical signature. This new understanding allows us to provide a different interpretation to the previously observed photoemission data for InP/GaP quantum wells and dots. We find analogous states in GaAs/AlAs and GaAs/GaP but now these levels are resonant within the continuum of states of the matrix conduction band and are therefore less pronounced.