  We report the magnetotransport properties up to 7 T in the organic highly
conducting Langmuir-Blodgett(LB) films formed by a molecular association of the
electroactive donor molecule bis(ethylendioxy)tetrathiafulvalene (BEDO-TTF) and
stearic acid CH$_3$(CH$_2$)$_{16}$COOH. We show the logarithmic decrease of dc
conductivity and the negative transverse magnetoresistance at low temperature.
They are interpreted in the weak localization of two-dimensional (2D)
electronic system based on the homogeneous conducting layer with the molecular
size thickness of BEDO-TTF. The electronic length with phase memory is given at
the mesoscopic scale, which provides for the first time evidence of the 2D
coherent charge transport in the conducting LB films.
