While the dynamics of model systems has been widely studied, the sizes of the systems has been limited. We present the dynamics for two large systems: a 9 degrees of freedom molecule and a 10000 state tier model. Classical non-linear resonance analysis and its quantum analog have been instrumental in providing insight into the pathways and rates of IVR processes in the overtone excitation of small molecules such as benzene and cyanoacetylene. It has been observed that the fourth overtone OH excitation of propargyl alcohol (PPA) is anomalously broad in comparison to the corresponding band of other small alcohols, possibly the result of rapid IVR out of the excited mode. An accurate model displayed no classical relaxation, but the quantum dynamics indicated an approximate degeneracy between the excited OH stretch and a combination band that can explain the observed broadening. To better understand the tier-to-tier relaxation process, an abstract model consisting of ten tiers of states was developed with the final tier representing the vibrational bath-states via a 50 state/cm\sp−1 state density. The survival dynamics showed irreversible relaxation out of the initial tier without the usual Poincare recursions. Interestingly, a calculation of the time-dependent spectrum showed the presence of only a few large features up to 720 fs which could not be attributed in a simple fashion to the dynamics of sub-models consisting the first n tiers. The early appearance and long persistence of a few broad bands implied the presence of "IVR resonances". In an attempt to elucidate these resonances, a imaginary damping function or optical potential was added to the model. An eigenvalue calculation on the resulting Hamiltonian did yield several long-lived resonances, and in fact, a spectrum calculated using only the first five resonances qualitatively reproduced the short pulse-length spectrum calculated from the original model. The "discovery" of these resonances is a step towards understanding and interpreting future pulselength dependent spectra in terms of the underlying tier structure of the systems studied.