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The nebular abundances in dwarf galaxies provide valuable clues to their star-formation histories. We have been engaged in an extensive observational study of actively star-forming blue compact dwarf galaxies (BCDs). Our program combines optical and NIR imaging, optical spectroscopy, and HI and CO radio data in an attempt to understand the status of star-formation and chemical evolution in these systems. Luminosities of the BCDs in our sample lie in the range M$_B$ = $-$13 -- $-$16.
\par We have obtained high-quality optical spectra of 21 BCDs for the purpose of deriving nebular abundances. We present values for the abundances of He, N, O, S, Ne, and Ar for this sample. In addition, we have estimated O and N abundances for a sample of 7 non-dwarf starburst galaxies of higher luminosity. For the BCD sample, we find that the N/O ratio remains constant at a mean value of 0.032 $\pm$ 0.004 with increasing O/H. This result, which extends over a factor of more than 10 in O/H, is indicative of the N being chiefly of primary origin in these systems. The value of N/O is observed to increase in the sample of larger starburst galaxies for log(O/H) above -3.5, consistent with previous studies. S/O and Ne/O are also both constant with increasing O/H, and have mean values of 0.032 $\pm$ 0.007 and 0.135 $\pm$ 0.013 respectively.
\par The BCD and starburst O/H values were used to calibrate an abundance sequence for a number of key emission-line diagnostic ratios which allow us to estimate metallicities for a large sample of emission-line galaxies (ELGs) to an accuracy of 0.1 -- 0.2 dex. The calibrations were applied to spectral data from two large published samples of ELGs from the Michigan and Case surveys. We use these data, representing nearly 200 individual galaxies, to investigate the existence of a metallicity-luminosity relationship for actively star-forming galaxies. We find the ELGs exhibit a relationship very similar to that found for more quiescent dwarf and Magellanic irregular galaxies by Skillman et al. (1989). The subsample of BCDs hosted by dwarf elliptical galaxies show systematically higher O/H at a given luminosity than the rest of the sample.
