  In this paper, we study the third-order nonlinear optical response due to
transitions between excitonic levels in two-dimensional transition metal
dichalcogeniedes. To accomplish this, we use methods not applied to the
description of excitons in two-dimensional materials so far and combined with a
variational approach to describe the $1s$ excitonic state. The aforementioned
transitions allow to probe dark states which are not revealed in absorption
experiments. We present general formulas capable of describing any third-order
process. The specific case of two-photon absorption in WSe2 is studied. The
case of the circular well is also studied as a benchmark of the theory.
