  Hall effect and magnetoresistance have been measured on single crystals of
$NdFeAsO_{1-x}F_{x}$ with x = 0 ($T_c$ = 0 $ $K) and x = 0.18 ($T_c$ = 50 $
$K). For the undoped samples, strong Hall effect and magnetoresistance with
strong temperature dependence were found below about 150 K. The
magnetoresistance was found to be as large as 30% at 15 K at a magnetic field
of 9 T. From the transport data we found that the transition near 155 K was
accomplished in two steps: first one occurs at 155 K which may be associated
with the structural transition, the second one takes place at about 140 K which
may correspond to the spin-density wave like transition. In the superconducting
sample with $T_c$ = 50 $ $K, it is found that the Hall coefficient also reveals
a strong temperature dependence with a negative sign. But the magnetoresistance
becomes very weak and does not satisfy the Kohler's scaling law. These
dilemmatic results (strong Hall effect and very weak magnetoresistance) prevent
to understand the normal state electric conduction by a simple multi-band model
by taking account the electron and hole pockets. Detailed analysis further
indicates that the strong temperature dependence of $R_H$ cannot be easily
understood with the simple multi-band model either. A picture concerning a
suppression to the density of states at the Fermi energy in lowering
temperature is more reasonable. A comparison between the Hall coefficient of
the undoped sample and the superconducting sample suggests that the doping may
remove the nesting condition for the formation of the SDW order, since both
samples have very similar temperature dependence above 175 K.
