  Dynamics of charge-density fluctuations in a system of two tunnel-coupled
wires contains two diffusion modes with dispersion iw=Dq^2 and iw
=Dq^2+2/tau_t, where D is the diffusion coefficient and tau_t is the tunneling
time between the wires. The dispersion of corresponding spin-density modes
depends on magnetic field as a result of spin precession with Larmour
frequency, w_L. The presence of two modes affects the shape of the Hanle curve
describing the spin-dependent resistance, R, between ferromagnetic strips
covering the non-magnetic wires. We demonstrate that the relative shapes of the
R(w_L)-curves, one measured within the same wire and the other measured between
the wires, depends on the ratio tau_t/tau_s, where tau_s is the spin-diffusion
time. If the coupling between the wires is local, i.e. only at the point x=0,
then the difference of the shapes of intra-wire and inter-wire Hanle curves
reflects the difference in statistics of diffusive trajectories which "switch"
or do not switch near x=0. When one of the coupled wires is bent into a loop
with a radius, a, the shape of the Hanle curve reflects the statistics of
random walks on the loop. This statistics is governed by the dimensionless
parameter, a/(D tau_s)^(1/2).
