With the aim of investigating galaxies with two strong simultaneous starbursts, we have extracted a sample of galaxies with double-peaked emission lines in their global spectra from the Sloan Digital Sky Survey (SDSS) spectral data base. We then fitted the emission lines Hα, Hβ, [O III]λ5007, [N II]λ6584, [S II]λ6717 and [S II]λ6731 of 129 spectra by two Gaussians to separate the radiation of the two (blue and red) components. A more or less reliable decomposition of all these emission lines has been found for 55 spectra. Using a standard Baldwin, Phillips & Terlevich (BPT) classification diagram, we have been able to divide the galaxies from our sample into two subsamples: Sample A consisting of 18 galaxies where both components belong to the photoionized class of objects, and Sample B containing 37 galaxies that show non-thermal ionization [active galactic nuclei (AGNs)]. We have examined the properties of the blue and red components, and found that the differences between radial velocities of components lie within 200-400 km s-1 for galaxies of both subsamples. The equivalent number of ionizing stars is in the range of 104-105 O7V stars for each component in the galaxies of Sample A. We have estimated the oxygen and nitrogen abundances as well as the electron temperatures for each component using the recent NS-calibration and from global spectra for galaxies from Sample A using both NS- and ON-calibration. We have found that the global oxygen abundance is typically in between the measured abundances of individual components for our sample of galaxies, and that both calibrations provide consistent global abundances. Finally, we suggest that the classical O/H-N/O diagram be used to test the reliability of the dividing lines between starburst-like objects and AGNs in the so-called BPT diagram.