This paper describes the aims, objectives and first results of the observational program for the study of distant core-collapse supernovae (SNe) with redshifts z < 0.3. This work is done within the framework of an international cooperation program on the SNe monitoring at the 6-m BTA telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences, and other telescopes. We study both the early phases of events (SN type determination, redshift estimation, and a search for manifestations of a wind envelope), and the nebular phase (the effects of explosion asymmetry). The SNe, associated with cosmic gamma-ray bursts are of particular interest. An interpretation of our observational data along with the data obtained on other telescopes is used to test the existing theoretical models of both the SN explosion, and the surrounding circumstellar medium. In 2009 we observed 30 objects; the spectra were obtained for 12 of them. We determined the types, phases after maximum, and redshifts for five SNe (SN 2009db, SN 2009dy, SN 2009dw, SN 2009ew, SN 2009ji). Based on the obtained photometric data a discovery of two more SNe was confirmed (SN 2009bx and SN 2009cb). A study of two type II supernovae in the nebular phase (SN 2008gz and SN 2008in) is finalized, four more objects (SN 2008iy, SN 2009ay, SN 2009bw, SN 2009de) are currently monitored.
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