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The ferroelectric switching in Langmuir-Blodgett films of poly (vinylidene fluoride trifluoroethylene) is studied. The films have a distribution of switching times several decades wide. Nearly a half of the film volume may be switched faster than 1 ms, though complete switching of a whole sample may require 100 s or more. The switching occurs through a domain nucleation and growth mechanism. The decay of polarization at zero bias is logarithmic in time, with a constant rate below 5% per decade at room temperatures. The coercive voltage may be as low as 5 V, which makes the films promising for use in nonvolatile random-access data storage.