The stability of the Landau-Fermi liquid theory is investigated. It has been shown that if the interaction function of the Fermi system is a finite function of the angle between the momenta of two particles at the Fermi surface, then the liquid can be stable. We have shown that the absolute value of the expansion coefficients of the interaction functions in Legendre polynomials are decreasing function of the coefficients indices. We solve the stability condition for one photon exchange (OPE) in an electron gas. The results show that we must use the massive boson propagator (higher order corrections to the photon propagator). Similar to previous works (Abrikosov et al. in Method of Quantum Field Theory in Statistical Physics, Pergamon, Elmsford, 1965), our result is proportional to g 2. The density and temperature dependence of results is occulted in the effective mass of the system. © 2011 Springer Science+Business Media, LLC.