  The formalism is developed for a tree-dimensional ($3D$) nonlinear
Stokes-Mueller polarimetry. The expressions are derived for the generalized
$3D$ linear and nonlinear Stokes vectors, and the corresponding nonlinear
Mueller matrix. The coherency-like Hermitian square matrix $X$ of
susceptibilities is introduced, which is derived from the nonlinear Mueller
matrix. The $X$-matrix is characterized by the index of depolarization. Several
decompositions of the $X$-matrix are introduced. The $3D$ nonlinear
Stokes-Mueller polarimetry formalism can be applied for three and higher wave
mixing processes. The $3D$ polarimetric measurements can be used for structural
investigations of materials, including heterogeneous biological structures. The
$3D$ polarimetry is applicable for nonlinear microscopy with high numerical
aperture objectives.
