  Using the exact diagonalization technique, we determine the energy spectrum
and wave functions for finite chains described by the two-spin
(Kugel--Khomskii) model with different types of intersubsystem exchange terms.
The found solutions provide a possibility to address the problem of quantum
entanglement inherent to this class of models. We put the main emphasis on the
calculations of the concurrence treated as an adequate numerical measure of the
entanglement. We also analyze the behavior of two-site correlation functions
considered as a local indicator of entanglement. We construct the phase
diagrams of the models involving the regions of nonzero entanglement. The
pronounced effect of external fields, conjugated to both spin variables on the
regions with entanglement, could both enhance and weaken the entanglement
depending on the parameters of the models.
