Two remarkable properties of the interior band of $ɛ$-solutions of a general nonlinear complementarity problem in $ℝ^n$ are studied. The study is based on the notion of scalar derivative and the notion of infinitesimal interior-point-$ɛ$-exceptional family for a function. This paper is a complementary part of the paper "Y. B. Zhao and G. Isac, Properties of a multivalued mapping associated with some nonmonotone complementarity problems, SIAM J. Control Optim., 39 Nr.2 (2000), pp. 571-593''.