A recent theory for the long time dynamics of flexible chain molecules is tested for the internal dynamics of triglycine and octaglycine, systems which are much more complicated than the previously studied alkanes. The theory extends the generalized Rouse (GR) theory used for the dynamics of polymers by providing a systematic procedure for including the contributions from internal friction and memory function matrices which are neglected in the GR theory. The mode-coupling method expresses the time correlation functions in terms of the eigenvalues and eigenfunctions of the diffusion operator and determines the eigenvalues by expanding the eigenfunctions in a suitable basis set. The greater complexity of the polyglycine interaction potential and the presence of cooperative local conformational transitions require including higher order mode coupling contributions than previously used. A major computational impediment induced by this requirement is the enormous growth in size of the basis set with the addition of the higher order mode coupling contributions that are needed to describe the influence of the memory functions. This impediment is alleviated by a new sorting procedure that includes in the basis set only the mode coupling functions with the slowest first order relaxation times. The theory is compared with Brownian dynamics (ED) simulations, so that both theory and simulation use identical, realistic potential functions and identical models for the solvent. The new method describes motions on time scales more than an order of magnitude longer than those accessible to molecular dynamics simulations. Inclusion of the memory functions greatly influences the dynamics, and the theory produces excellent agreement with the ED simulations for the long time motions. Individual ED trajectories exhibit the local and correlated conformational transitions.