  We report the temporal and spectral analysis of three thermonuclear X-ray
bursts from 4U 1608-52, observed by the Neutron Star Interior Composition
Explorer (NICER) during and just after the outburst observed from the source in
2020. In two of the X-ray bursts, we detect secondary peaks, 30 and 18 seconds
after the initial peaks. The secondary peaks show a fast rise exponential
decay-like shape resembling a thermonuclear X-ray burst. Time-resolved X-ray
spectral analysis reveals that the peak flux, blackbody temperature, and
apparent emitting radius values of the initial peaks are in agreement with
X-ray bursts previously observed from 4U 1608-52, while the same values for the
secondary peaks tend toward the lower end of the distribution of bursts
observed from this source. The third X-ray burst, which happened during much
lower accretion rates did not show any evidence for a deviation from an
exponential decay and was significantly brighter than the previous bursts. We
present the properties of the secondary peaks and discuss the events within the
framework of short recurrence time bursts or bursts with secondary peaks. We
find that the current observations do not fit in standard scenarios and
challenge our understanding of flame spreading.
