We calculate the four-wave-mixing signal of excitons generated at k(4) = k(1) + k(2) - k(3) by two pulsed entangled photon pairs (k(1), k(2))and(k(3), k(4)), where all four modes are chronologically ordered. Entangled photons offer an unusual combination of bandwidths and temporal resolution not possible by classical beams. Contributions from different resonances can be selected by varying the parameters of the photon wave function. The signal scales linearly rather than quadratically with the laser field intensity, which allows performance of the measurements at low powers.