  We study an interplay between the orbital degeneracy and spin-orbit coupling
giving rise to spin-orbital entangled states. As a specific example, we analyze
the interaction of electrons occupying triply degenerate single-ion $t_{2g}$
levels with trigonal vibronic modes (the $t\otimes T$ problem). A more general
problem of the electron-lattice interaction involving both tetragonal and
trigonal vibrations is also considered. It is shown that the result of such
interaction crucially depends on the occupation of $t_{2g}$ levels leading to
either the suppression or enhancement of the Jahn-Teller effect by the
spin-orbit coupling.
