Single (spinor) particle motions in randomly fluctuating U(1) and SU(2
) magnetic fluxes in two dimensions are compared. While the problems a
re similar in the weak-fluctuation limit, strikingly different physica
l behavior is found in the strong-fluctuation limit. The orbital susce
ptibility with respect to an external magnetic field vanishes in the s
trong-coupling U(1) limit, while in the SU(2) case a finite paramagnet
ic response exists, with an effective coupling constant 2e. Potential
applications of the results to spin liquids and other problems are dis
cussed.