The intersection \(P\) of a family \(\mathcal H\) of closed half-spaces of Euclidean space is called a pseudopolyhedron if for every \(x\in P\) there is a neighborhood of \(x\) having non-empty intersection with at most finite number of the bounding hyperplanes of the half-spaces from \(\mathcal H\). The author presents basic properties of pseudopolyhedra generalizing the proofs for polyhedra given in Section 2.6 and 3.1 of the book of \textit{B. Grünbaum} [Convex polytopes. London etc.: Interscience (1967; Zbl 0163.16603)]. The main result of the paper is an extension of the result of \textit{H. Bruggesser} and \textit{P. Mani} [Math. Scand. 29(1971), 197--205 (1972; Zbl 0251.52013)] to polyhedra complexes arising as boundary complexes of pseudopolyhedra.