  Low-mass X-ray binaries are binary systems composed of a compact object and a
low-mass star. Recently, a new class of these systems, known as symbiotic
$X$-ray binaries (with a neutron star with a M-type giant companion), has been
discovered. Here, we present long-duration ${\it XMM}$ observations of the
source 1RXS J180431.1-273932. Temporal and spectral analysis of the source was
performed along with a search for an optical counterpart. We used a
Lomb-Scargle periodogram analysis for the period search and evaluated the
confidence level using Monte-Carlo simulations. The source is characterized by
regular pulses so that it is most likely a neutron star. A modulation of
$494.1\pm0.2$ s (3$\sigma$ error) was found with a confidence level of $>$99%.
Evidence of variability is also present, since the data show a rate of change
in the signal of $\sim -7.7\times 10^{-4}$ counts s$^{-1}$ hr$^{-1}$. A longer
observation will be necessary in order to determine if the source shows any
periodic behavior. The spectrum can be described by a power law with photon
index $\Gamma\sim 1$ and a Gaussian line at 6.6 keV. The X-ray flux in the
0.2--10 keV energy band is $5.4\times 10^{-12}$ erg s$^{-1}$ cm$^{-2}$. The
identification of an optical counterpart (possibly an M6III red-giant star with
an apparent visual magnitude of $\simeq 17.6$) allows a conservative distance
of $\sim 10$ kpc to be estimated. Other possibilities are also discussed. Once
the distance was estimated, we got an $X$-ray luminosity of $L_X\ut<6\times
10^{34}$ erg s$^{-1}$, which is consistent with the typical $X$-ray luminosity
of a symbiotic LMXB system.
