  We present most general one-parametric solutions of the Yang-Baxter equations
(YBE) for one spectral parameter dependent $R_{ij}(u)$-matrices of the six- and
eight-vertex models, where the only constraint is the particle number
conservation by mod(2). A complete classification of the solutions is
performed. We have obtained also two spectral parameter dependent particular
solutions $R_{ij}(u,v)$ of YBE. The application of the non-homogeneous
solutions to construction of Zamolodchikov's tetrahedral algebra is discussed.
