Pseudoradial normal spaces of any order of pseudoradiality given by an ordinal number not greater than $\sigma_c(X)^+$ are constructed. Another construction with similar properties is given for compact $T_1$ spaces. Finally pseudoradial spaces of cardinality $\omega_{\alpha}$ and pseudoradial order $\omega_{\alpha+1}$ are exhibited. The most important tools to perform such constructions are those contained in Lemma 2.7, Theorem 2.8, Theorem 4.2 and Theorem 5.2.
