We consider ultra narrow-line lasers based on doubly-resonant fiber cavities, describe experimental techniques, and present two methods for passive stabilization of single-frequency fiber "rillouin lasers. In the first approach, "rillouin fiber laser is passively stabilized at the pump resonance frequency by employing the self-injection locking phenomenon. We have demonstrated that this locking phenomenon delivers a significant narrowing of the pump laser linewidth and generates the Stokes wave with linewidth of about . kHz. In the second methodology, the fiber laser is stabilized with an adaptive dynamical grating self-organized in un-pumped Er-doped optical fiber. The laser radiates a single-frequency Stokes wave with a linewidth narrower than Hz. The ring resonators of both presented lasers are simultaneously resonant for the pump and the Stokes radiations. For adjusting the double resonance at any preselected pump laser wavelength, we offer a procedure that provides a good accuracy of the final resonance peak location with ordinary measurement and cutting errors. The stable regime for both "rillouin lasers is observed during some intervals, which are interrupted by short-time jumping-intervals. The lasers' stability can be improved by utilizing polarization-maintaining PM fiber configuration and a cavity protection system.