Attractive electron correlations due to an electron-vibron interaction can overcome the direct Coulomb
repulsion of polarons in deformable molecular quantum dots (MQDs). If it happens, a switching appears in the
I-V characteristics of the degenerate nonadiabatic molecular bridges weakly coupled with electrodes providing
a route to ultrafast “memristors” (memory resistors) as the basis for future oscillators, amplifiers and other
important circuit elements. Here, we extend our theory of polaronic memristors to adiabatic MQDs strongly
coupled with leads to show that the degeneracy of MQD (or multilevel energy structure) along with the
polaron-polaron attraction is a vital ingredient of its switching behavior in the strong-coupling regime as well.