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Summary form only given. Experiments in semiconductor lasers subject to optical injection reveal unexpected periodic orbits as a function of the injection strength. It is well known that optical injection may destabilize the steady state of the laser and induce a Hopf bifurcation to sustained intensity oscillations at a frequency close to the relaxation frequency of the solitary laser. By further increasing the injection strength, period doubling bifurcations are then observed. We have found experimentally that period 3 orbits exist at injection levels close to the first period doubling bifurcation point This is clearly demonstrated by the optical spectrum. We have used a Fabry-Perot optical spectrum analyzer and two commercially available SDL lasers in a master-slave configuration. This nearby coexistence of period 3 and period 2 regimes has been observed for periodically modulated lasers.