  Sensitivity to temporal variation of the fundamental constants may be
strongly enhanced in transitions between narrow close levels of different
nature. This enhancement may be realized in a large number of molecules due to
cancelation between the ground state fine structure omega_f and vibrational
interval omega_v (omega=omega_f - n omega_v is close to zero, delta
omega/omega= K (2 delta alpha/alpha +0.5 delta mu/mu), K >>1, mu=m_p/m_e).
  The intervals between the levels are conveniently located in microwave
frequency range and the level widths are very small. Required accuracy of the
shift measurements is about 0.01-1 Hz. As examples, we consider molecules
Cl_2+, CuS, IrC, SiBr and HfF+.
