  We measure the magnetic penetration depth $\Delta\lambda(T)$ for
NdO$_{1-x}$F$_{x}$BiS$_{2}$ ($x$ = 0.3 and 0.5) using the tunnel diode
oscillator technique. The $\Delta\lambda(T)$ shows an upturn in the
low-temperature limit which is attributed to the paramagnetism of Nd ions.
After subtracting the paramagnetic contributions, the penetration depth
$\Delta\lambda(T)$ follows exponential-type temperature dependence at $T\ll
T_c$. Both $\Delta\lambda(T)$ and the corresponding superfluid density
$\rho_s(T)$ can be described by the BCS model with an energy gap of $\Delta(0)$
$\approx$ 2.0 $k_BT_c$ for both $x$ = 0.3 and 0.5, suggesting strong-coupling
BCS superconductivity in the presence of localized moments for
NdO$_{1-x}$F$_{x}$BiS$_{2}$.
