Bacteriophage T4L lysozyme (T4L) comprises two domains connected by a helical linker. Several methods detected ns domain motion associated with the binding of the peptidoglycan substrate. An ESR study of nitroxide-labeled T4L, based on the slowly relaxing local structure (SRLS) approach, detected ns local motion involving the nitroxide and the helix housing it. N-15-H spin relaxation data from T4L acquired at magnetic fields of 11.7 and 18.8 T, and 298 K, were analyzed previously with the model-free (MF) method. The results did not detect domain motion. SRLS is the generalization of MF. Here, we apply it to the same data analyzed previously with MF. The restricted local N-H motion is described in terms of tilted axial local ordering (S) and local diffusion (D-2) tensors; dynamical coupling to the global tumbling is accounted for. We find that D-2,D-perpendicular to is 1.62 x 10(7) (1.56 x 10(7)) s(-1) for the N-terminal (C-terminal) domain. This dynamic mode represents domain motion. For the linker D-2,D-perpendicular to N-terminal domain, the C-terminal domain, and the linker, respectively. This dynamic mode represents N-H bond vector fluctuations. The principal axis of D-2 is virtually parallel to the N-H bond. The order parameter, S-0(2), is 0.910 +/- 0.046 for most N-H bonds. The principal axis of S is tilted from the C-i-1(alpha)-C-i(alpha) axis by -2 degrees to 6 degrees for the N-, and C-terminal domains, and by 2.5 degrees for the linker. The tensorial-perspective-based and mode-coupling-based SRLS picture provides new insights into the structural dynamics of bacteriophage T4 lysozyme.