The second-order interference of two independent photons with different spectra in a Shih-Alley/Hong-Ou-Mandel interferometer is studied in Feynman’s path integral theory.There is a second-order interference patt for photons with different spectra if the photons are indistinguishable for the employed detection system.The conditions to observe the second-order temporal beating with photons of different spectra are analyzed.The influence of the response time of the detection system on the observed second-order interference patt is also discussed.It is a direct result of that measurement in quantum mechanics is dependent on the employed measuring apparatus.The results are helpful to understand the physics of two-photon interference in different schemes.