  We report the discovery of broad components with P-Cygni profiles of the
hydrogen and helium emission lines in the two low-redshift low-metallicity
dwarf compact star-forming galaxies (SFG), SBS 1420+540 and J1444+4840. We
found small stellar masses of 10^{6.24} and 10^{6.59} M$_\odot$, low oxygen
abundances 12+log O/H of 7.75 and 7.45, high velocity dispersions reaching
$\sigma$ ~700 and ~1200km/s, high terminal velocities of the stellar wind of
~1000 and ~1000-1700km/s, respectively, and large EW(H$\beta$) of ~300A for
both. For SBS 1420+540, we succeeded in capturing an eruption phase by
monitoring the variations of the broad-to-narrow component flux ratio. We
observe a sharp increase of that ratio by a factor 4 in 2017 and a decrease by
about an order of magnitude in 2023. The peak luminosity of ~10^{40}ergs/s of
the broad component in $L$(H$\alpha$) lasted for about 6 years out of a
three-decades monitoring. This leads us to conclude that there is probably a
LBV candidate (LBVc) in this galaxy. As for J1444+4840, its very high
$L$(H$\alpha$) of about 10^{41}ergs/s, close to values observed in active
galactic nuclei (AGNs) and Type IIn Supernovae (SNe), and the variability of no
more than 20 per cent of the broad-to-narrow flux ratio of the hydrogen and
helium emission lines over a 8-year monitoring do not allow us to definitively
conclude that it contains a LBVc. On the other hand, the possibility that the
line variations are due to a long-lived stellar transient of type LBV/SNIIn
cannot be ruled out.
