Using projection techniques we derive the equation of motion for the third-order nonlinear optical polarization of a strongly correlated system. We do not assume a Hartree-Fock ground state, but include the ground state correlations via time-independent interaction parameters and energies. Our theory can be used to describe the ultrafast nonlinear optical response of a strongly correlated cold electron gas, such as the two-dimensional electron gas in the quantum Hall effect regime. For this system, we show that the collective electronic excitations lead to a time-dependent coupling of the Landau level magnetoexcitons and a strong non-Markovian exciton dephasing. We discuss the signatures in the transient four-wave-mixing spectrum. . Most efforts so far have focussed on undoped semiconductors, where the lowest electronic excitations are the high energy interband e-h pair excitations that behave as quasiparticles with mutual interactions. In the absence of low lying electronic excitations, the ground state can be considered as rigid, and is usually described within the Hartree-Fock approximation. As a result, in undoped semiconductors, the role of the Coulomb correlations in the ultarafast nonlinear response can be studied in an exact fashion by using, e.g., the ''dynamics-controlled truncation scheme" (DCTS) [2].The DCTS considers a system with a Hartree-Fock ground state and assumes the absence of free carriers prior to the optical excitation [2]. Here we are interested in systems such as modulation-doped quantum wells (MDQWs) in a strong magnetic field, where a strongly correlated two-dimensional electron gas (2DEG) is already present in the ground state. The almost unexplored dynamics of strongly correlated systems, whose ground state electrons interact unadiabatically with the photo-excited e-h pairs, raises very fundamental questions. In MDQWs, the direct exciton-exciton interactions are screened. In the absence of magnetic field, the coherent nonlinear optical response was studied in Refs. [3,4] and shown to be strongly influenced by the interactions between the photoexcited carriers and the Fermi sea excitations.The role of the Coulomb correlations becomes more pronounced when a magnetic field is applied to the 2DEG in MDQWs, in a direction perpendicular to the quantum well plane. The energy