In this talk, we study some properties of solutions to the nonlinear complementarity problem (NCP($F,\mathbf{q}$)) where $F$ is a strictly diagonally isotone function or several related classes of functions. We prove that when $F$ is a strictly diagonally isotone function with $F(\mathbf{0})=\mathbf{0}$, then each nonzero solution of NCP($F,\mathbf{0}$) contains at least two nonzero components. Particularly, we consider two subclasses of the strictly diagonally isotone function: $M$-functions and the strongly strictly diagonally isotone functions. For NCP($F,\mathbf{q}$) with $F$ being an $M$-function, we show that it has the property of globally uniqueness and solvability if $F$ is also positively homogenous. For NCP($F,\mathbf{q}$) with $F$ being a strongly strictly diagonally isotone function, we show that its solution set is nonempty and compact if $F$ is also positively homogeneous; and then, some results are obtained on the uniqueness of solution set under some assumptions, especially the global uniqueness. In addition, we also introduce two new classes of functions: strongly diagonally isotone functions and strictly off-diagonally antitone functions, and show that when $F$ is both strongly diagonally isotone and strictly off-diagonally antitone, the concerned NCP($F,\mathbf{q}$) has at most one solution. At the same time, we introduce some examples which correspond to these new functions and come from tensor complementarity problems.