AB STRACT. A study of the viability of smal l populations of Hymenoptera is a matter of importance to gain a better zoological, ethological, genetical and ecological knowledge of these insects, and for conservati on purposes, mainl y because of the consequences to the survival of colonies of many species of bees, wasps, and ants. Based on the WHmNG ( 1943) principle, KERR & VENCOVSKJ ( 1982) presented a hypothesis that states that viable populations of stingless bees (Me liponini) should have at least 40 colonies to survive. This number was later extended to 44 colonies by KERR ( 1985). This wo uld be necessary to avoid any substantial amount of homozygosis in the pair o f chromosomic sexual loci, by keeping at least six different sex ual gene alleles in a reproducti ve populati on. In most cases this would prevent the producti on of useless diploid males. However, several facts weigh against considering this as a general rule. From 1990 to 200 1, 287 colony di visions were made, starting with 28 foundation co lonies, in the inbreeding and population experiments with the Meliponini reported here. These experiments constitute the most extensive and longest scientific research ever made with Meliponini bees. In ten di ffe re nt experiments presented here, seven species (one with two subspecies) of Meli ponini bees were inbred in fi ve localities inside the ir wide-reachi ng nati ve habitats, and in two localities far away from these habitats. Thi s was done fo r several years. On the whole, the nu mber of colonies increased and the loss of coloni es overthe years was smal l. In two of these experiments, al though these populations were far ( 1,000 km and 1,200 km) from their nati ve habitat, their foundati on colonies were multiplied successful y. It was possible to bui ld up seven strong and three expanding medium populations, starting with one, two, three or e ven fi ve colonies. However, in six other cases examined here, the WHmNG ( 1943) principl e and the hypothesis of KERR & VENCOVS KI ( 1982) and KERR (1985), possibly hold up . In two other cases, the results are still unclear. Outside native habitats, most inbreeding experiments failed, possibly because of conditions that cause ecological stress. Although much more data are still needed, a new working hypothesis on the molec ul ar level was presented to explain the results of the experiments described here. In the absence of any considerable stress, and in the eventual ity of a good nutritive situation, even indi vidual bees that are homozygous in the pai r of chromosomic sexual locus would prod uce a sufficient amount of a sex determining substance. Therefore, the female genes of all the diploid indi viduals of a colony, both homozygous and heterozygo us, wou ld be activated. However, situations of considerable stress wo ul d cause a poor physiological and nutritive condition. Th.is, togethe r with homozygos is in the pair of chromosomi c sexual loc us, would lead to a s maller production of the sex determining substance. When thi s happens in the dipl o...