Minke whales - the rorqual group of the family Balaenopteridae - are widely distributed and constitute an important major harvestable living resource of the sea. Recently, the Antarctic minke whale population has been estimated to be between 150,000 and 300,000. Populations being dynamic entities, the size of the minke whale population has been changing. Currently , the minke whale population in the Antarctic has been claimed to have increased considerably. However, the minke whale stock arriving off Brazil could be regarded as only a small discrete unit of breeding stock and an integral part of the Brazilian natural resource. Data analysis based on the past 21 years shows that this stock is relatively in a steady state, but with only a few annual fluctuations which are around a constant mean value; and these departures are attributable both to environmental conditions and the local operational parameters. Further, the analysis of overall data does not suggest any decline in the Brazilian stock and a MSY at about 58.5% can be taken without depleting the stock, provided no dramatic changes occur in the native Antarctic habitat where the minke whales return to feed. This would allow Brazil a carefully controlled rational utilization of this potentially valuable sea resource since enough exploitable numbers of minke whales have been estimated to be available for Area II. The current arguments of the conflicts between the Pro -and Anti-whaling groups are also briefly discussed.