  In many transition metal compounds, in particular those containing Fe^{2+}
and Co^{3+}, there occur spin-state transitions between low-spin and high-spin
(or intermediate-spin) states. We show that typical interactions between
similar spin-state ions are short-range repulsion, and long-range interaction
which can have different sign depending on the elastic anisotropy of the
lattice and on the direction between respective ions. Due to such character of
effective interactions at the spin-state transitions there may occur different
superstructures -- ordered arrangement of different spin-states, which in
particular may have the form of stripes. The properties of the system
TlSr_2CoO_5 for which such a superstructure was recently observed
experimentally, are discussed from this point of view.
