We present results of a search for variable stars in the intermediate-age open cluster NGC 7044. We found 23 variable stars in the observed field. One star turned out to be of the delta Sct type with two pulsational modes excited. From the position in the color-magnitude diagram we conclude that this star is a member of the cluster. Moreover, we found 13 eclipsing systems, of which five are W UMa stars, one is a beta Lyr variable, six are beta Per binaries showing detached configuration, and the last one is another probable beta Per system. Using the period-luminosity-color relation for W UMa stars we established the membership of the contact binaries, finding four of them to be very probable cluster members. We estimated from these four stars an apparent distance modulus (m-M)_V of NGC 7044 to be 14.2 +/- 0.4 mag, which is smaller than previous determinations of this parameter. We were able to derive orbital period for only four beta Per systems. For the remaining ones we observed only two or three eclipses. Finally, nine stars we found to show irregular light changes. Most of them are red stars not belonging to the cluster. For the cluster core we determined a reddening map, which allowed us to construct a dereddened color-magnitude diagram of NGC 7044 with a narrow main-sequence. By fitting a theoretical isochrone to this diagram we derived E(V-I_C) = 0.92 mag, (m-M)_V = 14.45 mag and log(age/yr) = 9.2.
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