The paper discusses the structural and semantic types of concessive constructions in the Altai language. In the Altai language use is made of specialized and non-specialized means for expressing concessive relations. The specialized means involve synthetical-analytical and analytical polypredicative constructions. These constructions uniquely express concessive relations. The main means of expressing concessive relations is a synthetical-analytical construction, the dependent predicate of which is expressed by the all-Turkic non-finite form =sa combined with the all-Turkic imphatic particle ta. This concessive construction is universal for all Turkic languages. The non-specialized means involve the synthetic constructions, whose main meaning is the expression of other types of relations. The meaning of concession is actualized at certain syntactic conditions.