We report the discovery of a systematic constant time lag between the X-ray and radio flares of the gamma-ray binary LSI +61 303, persistent over a long, multi-year timescale. Using the data from the monitoring of the system by RXTE we show that the orbital phase of X-ray flares from the source varies from φX ≃ 0.35 to φX ≃ 0.75 on the superorbital 4.6yr timescale. Simultaneous radio observations show that periodic radio flares always lag the X-ray flare by ΔφX - R ≃ 0.2. We propose that the constant phase lag corresponds to the time of flight of the high-energy particle-filled plasma blobs from inside the binary to the radio emission region at the distance of 10 times the binary separation distance. We put forward a hypothesis that the X-ray bursts correspond to the moments of formation of plasma blobs inside the binary system. © 2012. The American Astronomical Society. All rights reserved.