  We present results from a quantum and semiclassical theoretical study of the
$\rho_{xy}$ and $\rho_{xx}$ resistivities of a high mobility 2-D electron gas
in the presence of a dilute random distribution of tubes with magnetic flux
$\Phi$ and radius $R$, for arbitrary values of $k_f R$ and $F=e\Phi/h$. We
report on novel Aharonov-Bohm type oscillations in $\rho_{xy}$ and $\rho_{xx}$,
related to degenerate quantum flux tube resonances, that satisfy the selection
rule ${(k_fR)}^2=4F(n+{1\over 2})$, with $n$ an integer. We discuss possible
experimental conditions where these oscillations may be observed.
