Selection of soybean experimental lines for tolerance to Asian rust and seed yield Soybean is an economically important culture and Brazil is among the largest world producers. Asian rust, caused by the fungus Phakopsora pachyrhizi, is a relatively new disease in Brazil and can cause large losses in this culture, represented by yield decreases and increases in costs for fungicide applications. There are some sources of vertical resistance genes for this disease, but there are also cases of resistance breakdown for some of these main genes. Tolerance, defined as the capacity of plants to endure a pathogen attack without significant losses, is a complementary strategy that can be used to control rust. The objective of this research was to study tolerance to Asian rust in experimental genotypes derived from 45 crosses in a 10 x 10 diallel design developed at the Sector of Applied Genetics to Self-Pollinated Crops, Department of Genetics/ESALQ/USP through methods of estimation of the rust effect and of phenotypic stability in combinations of fungicide managements, locations and years, besides identifing promising lines for inclusion in future breeding programs. The experimental designs used were Federer's augmented blocks in 2011/12 and 2012/13 and a randomized block design stratified in sets in 2013/14. In each year and location two experiments were performed: management 1, with the application of fungicides to control rust and other fungal diseases, including late season leaf diseases; management 2, only controlling other fungal disease, excluding rust. The contrast between these two managements allowed for an estimate of tolerance. Besides that, the stability based on the best genotype (Pi) and ecovalence (Wi) measurements were also used to estimate relative tolerance between genotypes. In 2011/12 225 F 2:7 progenies were evaluated; in 2012/13 675 F 7:8 lines were evaluated and the best 225 F 7:9 lines were evaluated in 2013/14. The results let to the following conclusions: a) there was clear evidence of tolerance to Asian rust among and within crosses; b) the strategy of comparing different fungicide managements to estimate tolerance (rust effect) was useful, but suffered instability, presenting low correlations among years; c) the methods of superiority or stability based on the best genotype (bmg) and ecovalence complemented the information based on the rust effect and aided in the selection of tolerant lines; d) initial evaluations for rust severity (rust score NF1) had low precision and it was recommended to concentrate on rust tolerance evaluations after longer periods of infection (NF2 and NF3); e) tolerance estimated by means of hundred-seed weights had low correlation with tolerance estimated by seed yield, therefore the combined use of both criteria improved the efficiency of selection for tolerance and seed yield; f) in the simulated selection 48 promising lines were identified for rust tolerance and seed yield, corresponding to approximately 22% selection percentage.