  We identified two optical counterparts of brightest ultraluminous X-ray
Sources (ULXs) in galaxies NGC5474 and NGC3627 (M66). The counterparts in
Hubble Space Telescope images are very faint, their V magnitudes are 24.7 ($M_V
\approx -4.5$) and 25.9 ($M_V \approx -4.2$), respectively. NGC5474 X-1 changes
the X-ray flux more than two orders of magnitude, in its bright state it has
$L_X \approx 1.6 \times 10^{40}$ erg/s, the spectrum is best fitted by an
absorbed power-law model with a photon index $\Gamma \approx 0.94$. M66 X-1
varies in X-rays with a factor of ~2.5, its maximal luminosity being $2.0
\times 10^{40}$ erg/s with $\Gamma \approx 1.7$. Optical spectroscopy of the
NGC5474 X-1 has shown a blue spectrum, which however was contaminated by a
nearby star of 23 mag, but the counterpart has a redder spectrum. Among other
objects captured by the slit are a background emission-line galaxy (z=0.359)
and a new young cluster of NGC5474. We find that these two ULXs have largest
X-ray-to-optical ratios of $L_X/L_{opt}$ ~ 7000 for NGC5474 X-1 (in its bright
state) and 8000 for M66 X-1 both with the faintest optical counterparts ever
measured. Probably their optical emission originates from the donor star. If
they have super-Eddington accretion discs with stellar-mass black holes, they
may also have the lowest mass accretion rates among ULXs such as in M81 X-6 and
NGC1313 X-1.
