  We investigate the Drude model of spin dynamics in two-dimensional spin-orbit
coupled systems. In the absence of an applied electric field, the spin aligns
with the k-dependent effective magnetic field. The influence of disorder (the
momentum relaxation time $\tau$) on the system is considered. In the presence
of an electric field, the change in momentum causes a change in the effective
magnetic field. The in-plane spin can precess around the successive change in
the orientation of the effective magnetic field. We find that up to the linear
order of the electric field, the spin orientation undergoes Larmor-like and
non-Larmor like precession. Furthermore, we find that the non-Larmor motion
over a very short time ($t\ll\tau$) exactly equals the result obtained from the
Kubo formula. This means that the Kubo formula only captures the system's
response over a very short evolution. The spin-Hall conductivity for Larmor and
non-Larmor precession in the Rashba system is analytically calculated. We find
that the intrinsic spin-Hall current is not a universal constant and correctly
drops to zero when the Rashba spin-orbit coupling drops to zero. We also
calculate the time-averaged Larmor and non-Larmor spin-Hall conductivities
(SHCs) for the k-cubic Rashba system and compare them to experimental values.
The time-averaged Larmor SHC vanishes and the non-Larmor SHC is given by
$2.1(q/8\pi)$ which is very close to the experimental value $2.2(q/8\pi)$ by
Wunderlich et al. [Phys. Rev. Lett. {\bf 94}, 047204 (2005)].
