The NMR relaxation method is widely used in various biomedical applications. Investigation of model homopeptides is an important step for understanding of structure and NMR properties of more complex branched peptides based on lysine monomers, for example, dendrimers, dendrigrafts and dendritic polymer brushes. In this paper, we perform molecular dynamics simulation of two linear lysine peptides with the same number of lysine monomers but with different connection between them through α- or ε-peptide bonds. We obtained that the end-to-end distance and radius of gyration are smaller and radial density near the center of mass is essentially larger and decrease faster with radial distance for α-lysine peptide than for ε-lysine peptide. Orientational mobility of CH2 groups in both peptides could be described by second order orientational autocorrelation function and by spin-lattice NMR relaxation time. We calculated both functions and found that the relaxation of vector in side chains of α-lysine peptide is slightly faster in comparison with mobility of CH2 groups in main chain of ε-lysine peptide. Thus the big difference between the relaxation rates of these two types of CH2 groups in lysine dendrimers obtained recently both in NMR and in simulation is mainly due to dendrimer effect and not due to difference in position (side or main chain) of CH2 group in short linear lysine fragments. This result allows to use NMR for discrimination between α-lysine and ε-lysine peptides as well as between linear lysine peptides (or their mixtures) and lysine dendrimers.