We report the detection during the JEM-X/INTEGRAL observations of several X-ray bursters of series of close type I X-ray bursts consisting of two or three events with a recurrence time much shorter than the characteristic (at the observed mean accretion rate) time of matter accumulation needed for a thermonuclear explosion to be initiated on the neutron star surface. We show that such series of bursts are naturally explained in the model of a spreading layer of accreting matter over the neutron star surface in the case of a sufficiently high ($dot{M}geq 1times 10^{-9} M_{odot} mbox{yr}^{-1}$) accretion rate (corresponding to a mean luminosity $L_{rm tot}geq 1times 10^{37} mbox{erg s}^{-1}$). The existence of triple bursts requires some refinement of the model - the importance of a central ring zone is shown. In the standard model of a spreading layer no infall of matter in this zone is believed to occur.
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