Summary: The four types of invexity for locally Lipschitz vector-valued functions recently introduced by T. W. Reiland are studied in more detail. It is shown that the class of restricted

$K$-invex in the limit functions is too large to obtain desired optimization theorems and the other three classes are contained in the class of functions which are invex 0 in the sense of our previous joint paper with

*B. D. Craven* and

*T. D. Phuong* [‘A new class of invex multifunctions’, to appear]. We also prove that the extended image of a locally Lipschitz vector-valued invex function is pseudoconvex in the sense of

*J. Borwein* [SIAM J. Control Optimization 16, 512-522 (1978;

Zbl 0383.90109)] at each of its points.