Single crystal ESR measurements at 33.6 GHz (Q band) in the layered copper-amino acid complex bis (L-Phenylalaninato) copper (II), Cu (L-Phe)₂, are reported and compared with earlier results at 9.7 GHz (X band). Strong frequency-dependent effects were observed in the linewidth which were isolated by subtracting the Q-band data from the X-band ones. The difference data were least-squares fitted to a theoretical expression including non-secular contributions of the different interactions present in this exchange-coupled system, plus a secular contribution ('residual Zeeman') due to the existence of two copper sites with different orientations. The weight of non-secular contributions allowed us to estimate an exchange frequency omega e/2 pi =(10+or-2) GHz in Cu(L-Phe)₂, which involves the interaction with the six copper neighbours. The frequency related with the exchange interaction between non-equivalent copper neighbours only, omega e_AB/2 pi =(10.7+or-0.6)GHz, was calculated from the secular residual Zeeman contribution. These values indicate that the spin dynamics in Cu(L-Phe)₂ is mainly determined by the exchange interaction between non-equivalent copper neighbours.