Summary: This paper deals with the optimal control of a mathematical model for the evolution of a Low-Grade Glioma (LGG). We will consider a model of the Fischer-Kolmogorov kind for two compartments of tumor cells, using ideas from T. Galochkina et al. [Math. Biosci. 267, 1–9 (2015; Zbl 1371.92063)] and V. M. Pérez-García [“Mathematical models for the radiotherapy of gliomas”, Preprint, 2012]. The controls are of the form \((t_1, \dots, t_n; d_1, \dots, d_n)\), where \(t_i\) is the \(i\)-th administration time and \(d_i\) is the \(i\)-th applied radiotherapy dose. In the optimal control problem, we try to find controls that maximize, in an admissible class, the first time at which the tumor mass reaches a critical value \(M_{*}\). We present an existence result and, also, some numerical experiments (in the previous paper [the first author and the third author, Comput. Appl. Math. 37, No. 1, 745–762 (2018; Zbl 1397.49064)], we have considered and solved a very similar control problem where tumoral cells of only one kind appear).