We study effects of strong fluctuations on the transport properties of superconductors near the classical critical point. In this regime conductivity is set by the delicate interplay of two competing effects. The first is that strong electron-electron interactions in the Cooper channel increase the lifetime of fluctuation Cooper pairs and thus enhance conductivity. On the other hand, quantum pair-breaking effects tend to suppress superconductivity. An interplay between these processes defines new temperature regime, Gi≲(T-Tc)/(Tc)≲Gi , where fluctuation induced transport becomes more singular, here Gi is the Ginzburg number. The most singular contributions to the conductivity stem from the dynamic Aslamazov-Larkin term, and interesting Maki-Thompson and interference corrections. The crossover temperature TcGi from weakly to strongly fluctuating regime is generated self-consistently as the result of scattering on dynamic variations in the order parameter. We suggest that the way to probe nonlinear fluctuations in superconductors is by magnetoconductivity measurements in the perpendicular field.