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We present high-quality ground-based spectroscopic observations of 54 supergiant H II regions in 50 low-metallicity blue compact galaxies with oxygen abundances 12 + log O/H between 7.1 and 8.3. We use the data to determine abundances for the elements N, O, Ne, S, Ar and Fe. We also analyze Hubble Space Telescope (HST) Faint Object Spectrograph archival spectra of 10 supergiant H II regions to derive C and Si abundances in a subsample of 7 BCGs. The main result of the present study is that none of the heavy element-to-oxygen abundance ratios studied here (C/O, N/O, Ne/O, Si/O, S/O, Ar/O, Fe/O) depend on oxygen abundance for BCGs with 12 + log O/H < 7.6 (Z < Zsun/20). This constancy implies that all these heavy elements have a primary origin and are produced by the same massive (M > 10Msun) stars responsible for O production. The dispersion of the C/O and N/O ratios in these galaxies is found to be remarkably small, being only +/-0.03 dex and +/-0.02 dex respectively. This very small dispersion is strong evidence against any time-delayed production of C and primary N in the lowest-metallicity BCGs (secondary N production is negligible at these low metallicities). The absence of a time-delayed production of C and N is consistent with the scenario that galaxies with 12 + log O/H < 7.6 are undergoing now their first burst of star formation, and that they are therefore young, with ages not exceeding 40 Myr. If very low metallicities BCGs are indeed young, this would argue against the commonly held belief that C and N are produced by intermediate-mass (3Msun < M < 9Msun) stars at very low metallicities, as these stars would not have yet completed their evolution in these lowest metallicity galaxies.