Precise spatiotemporal sequences of neuronal discharges (i.e., intervals between epochs repeating more often than expected by chance), have been observed in a large set of experimental electrophysiological recordings. Sensitivity to temporal information, by itself, does not demonstrate that dynamics embedded in spike trains can be transmitted through a neural network. This study analyzes how synaptic transmission through three archetypical types of neurons (regular-spiking, thalamo-cortical and resonator), simulated by a simple spiking model, can affect the transmission of precise timings generated by a nonlinear deterministic system (i.e., the Zaslavskii mapping in the present study). The results show that cells with subthreshold oscillations (resonators) are very sensitive to stochastic inputs, and are not a good candidate for transmitting temporally coded information. Thalamo-cortical neurons may transmit very well temporal patterns in the absence of background activity, but jitter accumulates along the synaptic chain. Conversely, we observed that cortical regular-spiking neurons can propagate filtered temporal information in a reliable way through the network, and with high temporal accuracy. We discuss the results in the general framework of neural dynamics and brain theories.