  The quantum levels population behavior of the two coupled flux qubits
depending on the external driving field characteristics is studied. The
explicit expressions for the multiphoton transition probabilities at an
arbitrary control field amplitude is obtained for the case of small tunnel
splitting energies. We describe the controllable features of their formation
and thereby creating or destroying entanglement by system bias tuning on the
direct inter-level transition and during the transition through intermediate
states. We found a feature of the qubits population inverting that ends in the
independence of the resonances positions from the qubits coupling strength.
Using Floquet--Markov equation we numerically demonstrate, that the positions
of multiphoton resonances are stable to dissipative processes.
