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Abundances of Li, heavy elements and carbon isotope ratios have been measured in 12 J-type galactic carbon stars. The abundance analysis shows that in these stars the abundances of s-process elements with respect to the metallicity are nearly normal. Tc is not present in most of them, although upper limits have been derived for WZ Cas and WX Cyg, perhaps two SC-type rather than J-type carbon stars. The Rb abundances, obtained from the resonance 7800 {\AA} Rb I line, are surprisingly low, probably due to strong non-LTE effects in the formation of this line in cool carbon-rich stars. Lithium and $^{13}$C are found to be enhanced in all the stars. These results together with the nitrogen abundances and oxygen isotope ratios measured by Lambert et al. (1986) and Harris et al. (1987) are used to discuss the origin of J-stars. The luminosity and variability class of the stars studied would indicate that they are low mass (M$\leq 2-3$ M$_\odot$), less evolved objects than the normal carbon stars, although the presence of some luminous (M$_{bol}<-5.5$) J-stars in our galaxy (WZ Cas may be an example) and in other galaxies, suggests the existence of at least two types of J-stars, with different formation scenarios depending upon the initial mass of the parent star. Standard evolutionary AGB models are difficult to reconcile with all the observed chemical characteristics. In fact, they suggest the existence of an extra-mixing mechanism which transports material from the convective envelope down to hotter regions where some nuclear burning occurs. This mechanism would act preferably on the early-AGB phase in low-mass stars. Mixing at the He-core flash and the binary system hypothesis are also discussed as alternatives to the above scenario.