Trawl fishing in slope waters of southern and southeastern sectors of Brazilian coast has been sustained by important concentrations of the gulf hake (Urophycis mystacea), argentine hake (Merluccius hubbsi), silver John dory (Zenopsis conchifera), monkfish (Lophius gastrophysus) and, seasonally, the argentine squid (Illex argentinus). Potential yields were estimated for the former four species using growth, natural mortality and selectivity parameters available in the literature or calculated from empirical relationships and length frequency distributions of the trawl catches. These potentials oscillated between 8 and 10% of the total virginal biomass (Bo ) and the total virginal exploitable biomass (ExBo ,) for the gulf hake and the argentine hake. In relation to the siver John dory estimated maximum catches corresponded to 12.5% of ExBo , and 9.5% of Bo , whereas in the monkfish these catches were limited to 6% of both ExBo , and Bo ,. Because the available biomass estimated for these stocks in the slope waters of southeastern and southern Brazil cannot be considered as virginal, at least for the gulf hake and the argentine hake, the estimated potential yields may be generally regarded as conservative reference points. They suggest that precautionary annual catches of the main targets combined (gulf hake, the argentine hake and the silver John dory) should be under 10% of their total biomass available. Additionally, regarding the monkfish, an important component of the trawl bycatch and the main target of a gill net fishery in the same area, the TAC (Total Allowable Catch) adopted for management purposes is well bellow (2,5%) the maximum levels estimated by life-history parameters.