Safflower is a rare culture adapted for growing in arid regions. It has wide usage as decorative, feeding plant and in medicine but mainly it is used in oil production nowadays. In rain insufficient areas in summer months it can be used as alternative to sunflower. Because of climate changes the study of the culture becomes even more important. The safflower plant (Carthamus tinctorius L) of the family of Asteraceae is one of the oilseeds growing in Asia, America, on the territory of Ukraine. Safflower is used as a forage plant for animals and birds, for technical, decorative purposes, in medicine. Safflower is a rough, herbaceous, annual plant with a pronounced appearance of an inhabitant of dry steppes. It is believed that the habitat of this species is confined to steppes and semi-deserts. The root of safflower is pivotal, it gives the plant the opportunity to feel good in arid climates. The stem is hard, branching, whitish in color, up to 100 cm tall, sometimes more. The leaves are alternate, sessile, oblong-lanceolate, leathery, with sharp edges, which usually end with spines, although there are varieties without spines, with a sharply protruding network of veins from below. According to available data, one recessive gene causes erectoid location of branches. Researchers Fernandez-Martinez and Knowles point to the existence of two genes that have the opposite effect on the location of branches. The ap gene in the homozygous state causes the branches to tilt at an angle of 20 degrees or less relative to the stem, and the dec gene from 80 to 90 degrees. The combination of these genes gives the slope of the branches to the stem in 40-70 degrees. The Institute of Oilseed Crops NAAS of Ukraine has been engaged in cultivation of safflower since 2001. The aim of this work was to study the inheritance of branch position on the stem and the association of plant height and rosette habit of samples in our collection. For realization of the work were used the methods of field experiment, genetic analysis and mathematical statistics. For determining the type of inheritance the results of free and artificial pollination were used. Chi-square test was used as a statistical method. Four samples from our collection heterogeneous by height, branch position and rosette habit were involved in crosses: Belotsvetkovy nekoluchy, Salut, Medovy, Kurchavy. Characteristics of crossed collection samples: Belotsvetkovy nekoluchy — normal branch position, medium height, average rosette habit; Salut — erectoid branch position, high, late rosette habit; Medovy — normal branch position, medium height, average rosette habit; Kurchavy — normal branch position, medium height, average rosette habit. The first generation from the free pollination of the plant with normal branch position in 2011 also had normal branch position, the second generation demonstrated splitting by 3:1 scheme into normal and wide branch position accordingly. In crossing plants with normal and erectoid branch position the first generation hybrids also had normal branch position, the second generation demonstrated splitting by 3:1 scheme into plants with normal and erectoid branch position. When crossing the sample Salut (high, late rosette habit) with Kurchavy sample (medium height, average rosette habit) the first generation hybrids were of medium height and average rosette habit. The second generation splitting scheme validly differed from the expected one 9:3:3:1. Genes encoding these traits are not fully linked. Using the formula r = n/N, where n is the number of recombinants and N is the total number of specimen, we calculated the crossover frequency. Thus, the sing of the normal branch position dominates wide and erectoid branch position sings in safflower. The sing of the rosette habit is linked with plant height sing. The distance between genes is 6,13 morganite.