  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 ($\dot{M}\geq 1\times 10^{-9}\ M_{\odot}\ \mbox{yr}^{-1}$)
accretion rate (corresponding to a mean luminosity $L_{\rm tot}\geq 1\times
10^{37} \mbox{erg s}^{-1}$). 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.
