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The series combination of a semiconductor diode gain element (a diode laser whose end facets have been antireflection coated) and an optical fiber has been placed inside an external cavity and the combined system has lased in a single spectral line whose width was less than the -nm (7.5-MHz) resolution of the scanning Fabry-Perot interferometer used in the measurement. This result has been achieved with either a single-mode or a multimode optical fiber in series with the diode gain element and for experiments in which a polarizer, oriented so its polarization is parallel to the diode gain element polarization, was placed at the other end of either fiber. The output of the external cavity is temporally stable as measured both by a 225-MHz-bandwidth detector system and a spectrum analyzer. Over a one minute interval the maximum fluctuation in the output frequency of the external cavity was found to be 2 MHz. Analysis of the threshold behavior of the external cavity for the cases where the multimode or single-mode fiber are in the cavity indicates that the coupling coefficients for either fiber are nearly the same. Without an external cavity, the coupling coefficient from the diode gain element (or from a similar, not anti-reflection-coated, laser) to the multimode fiber is over five times larger than that to the single-mode fiber. These coupling results are explained by postulating that for the multimode fiber, only one or a selected number of the many modes of the fiber can participate in the laser action of the external cavity. It is believed that only these mode(s) are reflected back into the fiber by the spherical mirror in appropriate phase and angle to participate in the laser emission.