The dynamic properties of meshlike polymer networks are considered using the cubic network of multisegmental "bead and spring" Rouse chains. The normal mode treatment is used. Rigorous expressions for the mean-square displacements of elements of the Gaussian network (junctions and nonjunction beads) are obtained. The autocorrelation functions of chain vectors between neighboring nonjunction beads (subchain vectors) and of end-to-end chain vectors between neighboring junctions are calculated. The time dependence of the relaxation modulus of a network is also considered. Contributions of intra- and interchain relaxation processes to various dynamic characteristics of a Gaussian network are compared. The time behavior of dynamic quantities obtained is estimated for different scale motions. It is shown that the relaxation of regular polymer networks consisting of long multisegmental Gaussian chains can be considered as a superposition of four different types of relaxation processes. These are the relaxation of network, chains with fixed junctions, the relaxation of chains with free ends, the relaxation processes in the intermediate region of the spectrum, and interchain cooperative network motions. The possibility of describing low-frequency dynamic properties of networks by a simplified coarse-grained network model used previously is proved.