Summary: The present paper gives characterizations of radially u.s.c. convex and pseudoconvex functions \(f: X\to\mathbb{R}\) defined on a convex subset \(X\) of a real linear space \(\mathbb{E}\) in terms of first- and second-order upper Dini-directional derivatives. Observing that the property \(f\) radially u.s.c. does not require a topological structure of \(\mathbb{E}\), we draw the possibility to state our results for arbitrary real linear spaces. For convex functions we extend a theorem of \textit{L. R. Huang} and \textit{K. F. Ng} [Math. Oper. Res. 22, No. 3, 747--753 (1997; Zbl 0886.49018)]. For pseudoconvex functions we generalize results of \textit{W. E. Diewert}, \textit{M. Avriel} and \textit{I. Zhang} [J. Econ. Theory 25, 397--420 (1981; Zbl 0483.26007)] and \textit{J.-P. Crouzeix} [Nonconvex Optim. Appl. 27, 237--256 (1998; Zbl 0931.90036)]. While some known results on pseudoconvex functions are stated in global concepts [e.g., \textit{S. Komlósi}, Math. Program. 26, 232--237 (1983; Zbl 0541.90081)], we succeeded in realizing the task to confine to local concepts only.