We report the,observation of Shubnikov-de Haas (SdH) oscillations in the mi
xed state of the organic superconductor beta"-(BEDT-TTF)(2)SF5CH2CF2SO3 (T(
c)approximate to4.4 K). At low temperatures the SdH oscillations per sist c
learly below the upper critical field B-c2(0)approximate to3.6 T almost dow
n to the field where the resistivity vanishes. Rather unusually, no additio
nal damping of the SdH-signal amplitude - as well as of the de Haas-van Alp
hen amplitude - is observed in the superconducting state. This indicates th
at the damping in the vortex state of this quasi-two-dimensional supercondu
ctor is different in character to that observed for most three-dimensional
materials.