Chain length and site dependencies of amide I local mode frequencies of alpha-helical polyalanines are theoretically studied by carrying out semiempirical quantum chemistry calculations. A theoretical model that can be used to quantitatively predict both the local amide I mode frequencies and coupling constants between two different local amide I modes is developed. Using this theoretical model and performing molecular dynamics simulation of an alpha-helical polyalanine in liquid water, we investigate conformational fluctuation and hydrogen-bonding dynamics by monitoring amide I frequency fluctuations. The instantaneous normal-mode analysis method is used to obtain densities of states of the one- and two-exciton bands and to quantitatively investigate the extent of delocalization of the instantaneous amide I normal modes. Also, by introducing a novel concept of the so-called weighted phase-correlation factor, the symmetric natures of the delocalized amide I normal modes are elucidated, and it is also shown that there is no unique way to classify any given amide I normal mode of the alpha-helical polyalanine in liquid water to be either A-mode-like or E-1-mode-like. From the ensemble-averaged dipole strength spectrum and density of one-exciton states, the amide I infrared absorption spectrum is numerically calculated and its asymmetric line shape is theoretically described. Considering both transitions from the ground state to one-exciton states and those from one-exciton states to two-exciton states, we calculate the two-dimensional IR pump-probe spectra and directly compare them with recent experimental results. A brief discussion on the cross-peaks previously observed in the two-dimensional difference spectrum is presented.