The Lang and Kobayashi equations modeling a semiconductor laser subject to optical feedback admit time-periodic solutions which are combinations of two distinct external cavity modes. We construct these solutions analytically and show that they emerge and disappear at two distinct Hopf bifurcation points. These mixed external cavity mode solutions exhibit interesting high frequency time-periodic intensities. Furthermore, they undergo a secondary bifurcation to quasiperiodic oscillations which we investigate numerically. Our analysis complements earlier investigations by Tager and Peterman (IEEE J. of Quant. Electron. 30 (1994) 1553) and provide a first explanation of recent experimental observations for a diode laser subject to two optical feedbacks.