  The geometric models of N=4 supersymmetric mechanics with
$(2d.2d)_{\DC}$-dimensional phase space are proposed, which can be viewed as
one-dimensional counterparts of two-dimensional N=2 supersymmetric sigma-models
by Alvarez-Gaum\'e and Freedman. The related construction of supersymmetric
mechanics whose phase space is a K\"ahler supermanifold is considered. Also,
its relation with antisymplectic geometry is discussed.
