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A multipoint fiber laser sensor, which consists of two cavities coupled based in three Bragg gratings of fiber optics and interrogated by the longitudinal mode beating frequency is presented. We used one Bragg grating (reference) and two Bragg gratings (sensors), which have the lowest reflection wavelength. The reference grating with the two sensors grating make two cavities: first one is the internal cavity which has 4230 m of length and the next one is the external cavity which has 4277 m of length. Measuring the laser beating frequency with a radio frequency (rf) analyzer for a resonance cavity and moving the frequency peaks when the another cavity are put in resonance, we prove that the arrangement can be used as a two points sensor for determining the difference of temperature or stress between these two points. On the other hand, one principal peak and three harmonics with bandwidths of 52Hz were obtained with the rf analyzer. Their bandwidth was controlled by an intra-cavity fiber Optical Delay Line (ODL) and was measured with the rf analyzer.