We present CCD broad band photometric observations in the fields of the Third Galactic Quadrant open clusters NGC 2580 and NGC 2588 ($V(I)_C$ and $UBV(RI)_C$ respectively). From the analysis of our data we found that NGC 2580 is located at a distance of about 4 kpc and its age is close to 160 Myr. As for NGC 2588, it is placed at about 5 kpc from the Sun and is 450 Myr old. This means that NGC 2588 belongs to the extension of the Perseus arm, whereas NGC 2580 is closer to the local arm structure. The luminosity functions (LFs) have been constructed for both clusters down to $V sim 20$ together with their initial mass functions (IMFs) for stars with masses above $M sim 1-1.5 M_{sun}$. The IMF slopes for the most massive bins yielded values of $x approx 1.3$ for NGC 2580 and $x approx 2$ for NGC 2588. In the case of this latter cluster we found evidence of a core-corona structure produced probably by dynamical effect. In the main sequences of both clusters we detected gaps, which we suggest could be real features.
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