Interference has been observed in the mixing of signal photons produced by spontaneous down-conversion in two nonlinear crystals, when the optical path difference through the interferometer greatly exceeds the coherence length of the light. The interference shows up as a periodic modulation of the spectrum. We demonstrate that the interference is nonclassical and connected with the entangled state of the signal and idler photons, by inserting the long delay in the path of the idler photons, even though the signal photons are interfering.