In the papers [1] and [2] a near-lattice was defined as a bisemilattice $(Q,\nabla,\Delta)$ satisfying the identity: \[ x\Delta(yabla zabla x)=(x\Delta y)abla(x\Delta z)abla(x\Delta x) \] This structure is called here a $(\Delta,\nabla)$-weak-distributive bisemilattice, and the structure satisfying the dual identity is said here to be a $(\nabla,\Delta)$-weak-distributive bisemilattice. In this paper a near-lattlce Is defined as a bisemilattice which satisfies the Identity \[ xabla(y\Delta x)=(xabla y)\Delta x. \] Some properties of such structures are proved, and a necessary and sufficient condition for a bisemilattice to be a near-lattlce is given.