  We report our findings on a new quasi-periodic oscillation (QPO) and a long
period from the ultraluminous X-ray source (ULX) X-2 in nearby galaxy NGC 4736
based on the Chandra and XMM-Newton archival data. To examine the timing
properties, power density spectra of the source have been obtained using Fast
Fourier Transform. Also the spectral parameters of the source have been
calculated by obtaining and fitting the energy spectra. Power density spectrum
of this source reveals a QPO peak at $0.73_{-0.14}^{+0.16}$ mHz with an
fractional rms variability of 16% using the Chandra data (in the year
2000-lower state of the source). The XMM-Newton data analysis indicates a peak
at $0.53_{-0.35}^{+0.09}$ mHz with a fractional rms variation of 5% (in the
year 2006-higher state of the source). These recovered QPOs overlap within
errors and may be the same oscillation. In addition, we detect a long
periodicity or a QPO in the Chandra data of about $(5.2\pm2.0)\times10^{-5}$ Hz
($\sim$ 5.4 hrs) over 3 $\sigma$ confidence level. If this is a QPO, it is the
lowest QPO detected from a ULX. The mass of the compact object in ULX X-2 is
estimated using the Eddington luminosity and a disk blackbody model in the
range (10$-$80) M_{\sun}.
