We perform the first calculations of frequency-dependent first hyperpolarizabilities in the second-order Moller-Plesset perturbation theory (MP2) as analytical third derivatives of the time-averaged MP2 quasienergy with respect to electric field strengths. The calculations of frequency-dependent first hyperpolarizabilities using the quasienergy derivative (QED) method-based MP2 (QED-MP2) response theory are presented for the electro-optic Pockels effect (EOPE) [beta(-omega;omega,0)] and second harmonic generation (SHG) [beta(-2 omega;omega,omega)] of the FH, H2O, CO, and NH3 molecules. The QED-MP2 values of the SHG first hyperpolarizabilities beta(parallel to)(-2 omega;omega,omega) for the H2O, CO, and NH3 molecules show good agreement with the experimental values. The QED-MP2 response theory is the simplest in ab initio methods for including dynamical electron correlation effects in dynamic response properties efficiently.