In this work we present nonequilibrium molecular dynamics simulation results for the Lyapunov spectra of atomic fluids confined in narrow channels of the order of a few atomic diameters. We show the effect that realistic walls have on the Lyapunov spectra. All the degrees of freedom of the confined system have been considered. Two different types of flow have been simulated: planar Couette flow and planar Poiseuille flow. Several studies exist on the former for homogeneous flows, so a direct comparison with previous results is performed. An important outcome of this work is the demonstration of how the spectrum reflects the presence of two different dynamics in the system: one for the unthermostatted fluid atoms and the other one for the thermostatted and tethered wall atoms. In particular the Lyapunov spectrum of the whole system does not satisfy the conjugate-pairing rule. Two regions are instead distinguishable, one with negative pairs’ sum and one with a sum close to zero. To locate the different contributions to the spectrum of the system, we computed “approximate” Lyapunov exponents belonging to the phase space generated by the thermostatted area and the unthermostatted area alone. To achieve this, we evolved Lyapunov vectors projected into a reduced dimensional phase space. We finally observe that the phase-space compression due to the thermostat remains confined into the wall region and does not significantly affect the purely Newtonian fluid region.