The three-dimensional diffusion in condensed material of a rotating and translating asymmetric-top molecule is considered with use of three frames of reference: the laboratory frame (x,y,z), a rotating frame (1,2,3)', and a moving frame (1,2,3). The frame (1,2,3)' has the same origin as (x,y,z), but rotates with an angular velocity \ensuremath{\omega}, the molecular angular velocity. The frame (1,2,3) is defined by the principal molecular moments of inertia, and its origin is therefore the molecular center of mass. The molecular angular velocity \ensuremath{\omega} is the same in all three frames. By writing a pair of simultaneous single-molecule Langevin equations, a rotational equation in (1,2,3) and a translational equation in frame (1,2,3)', a natural description of the molecular diffusion is obtained without the need of friction cross terms. This description introduces into the analysis the center-of-mass position vector r, and the forces obtained by transforming Newton's equation into a noninertial frame, i.e., by the frame transformation (x,y,z)\ensuremath{\rightarrow}(1,2,3)' or vice versa.These are the Coriolis force 2m\ensuremath{\omega}\ifmmode\times\else\texttimes\fi{}v, the centripetal force m\ensuremath{\omega}\ifmmode\times\else\texttimes\fi{}(\ensuremath{\omega}\ifmmode\times\else\texttimes\fi{}r), and the force m\ensuremath{\omega}\ifmmode \dot{}\else \.{}\fi{}\ifmmode\times\else\texttimes\fi{}r. The analysis also implies the consideration of the velocity \ensuremath{\omega}\ifmmode\times\else\texttimes\fi{}r. Here v is the molecular center-of-mass linear velocity, \ensuremath{\omega} the angular velocity, and r the position vector of the center of mass. It is shown by computer simulation that autocorrelation and cross-correlation functions of these terms can exist both in frame (x,y,z) and in frame (1,2,3), the moving frame. Examples are provided in the liquid state for the achiral asymmetric top dichloromethane and for the enantiomers and racemic mixture of bromochlorofluoromethane at two state points. The symmetry properties of some of the new cross-correlation functions are tabulated. Finally, experimental methods are suggested for observing cross-correlation functions such as these and for testing experimentally the detailed numerical paradigm provided by these computer simulations. Examples of one method are given with reference to the far-infrared power absorption of the tris(acetylacetonate) complexes of cobalt and chromium in the powdered crystalline state.