Enhanced internal mobility in proteins is typically functional. Domain motion in enzymes, necessarily related to catalysis, is a prototype in this context, Experimental N-15 spin relaxation data from E. coli adenylate kinase report qualitatively on nanosecond motion experienced by the domains AMPbd and LID. Previous quantitative analysis based on the mode-coupling slowly relaxing local structure approach confirmed nanosecond mobility but yielded unduly small local ordering and local geometry not interpretable directly in terms of the local protein structure. Here, we show that these features ensue from having assumed axial local ordering and highly axial local diffusion. After eliminating these simplified second-rank tensor properties, a physically sound picture, with the local motion interpretable as domain motion, is obtained. Rhombic local ordering, with components given by = 0.471, = -0.952 and = 0.481, and main ordering axis, Y-M, lying along C-1-1(alpha) - C-1(alpha), has been determined. The associated rhombic potential is given by axial (rhombic) coefficients of = -3.3 ( = 17.8). The average correlation time for domain motion is 10.4 (6.4) ns at 288 (302) K; the corresponding correlation time for global motion is 20.6 (14.9) ns. The rates for domain motion exhibit noteworthy Arrhenius-type temperature-dependence, yielding activation energies of 63.8 +/- 7.0 (53.0 +/- 9.1) kJ/mol for the AMPbd (LID) domain. The traditional model-free analysis ignores mode-coupling and simplifies tensor properties. Within its scope, the AKeco backbone emerges as largely rigid, approximate to 0.94; the main ordering axis, Z(M), lies along N-H, approximate to 16 (c(2)(2) = 0); and the slow local motional correlation time lies at the low end of the nanosecond time scale.