Triazolopyrimidines of the formula I where the index and the substituents are as defined below: R1 is C1-C10-alkyl, C2-C10-alkenyl, C2-C10-alkynyl, C3-C10-cycloalkyl, C3-C10-cycloalkenyl, phenyl, naphthyl, or a five- to ten-membered saturated, partially unsaturated or aromatic heterocycle which is attached via carbon to the triazolopyrimidine and contains one to four heteroatoms from the group consisting of N, O and S; R2 is C1-C4-alkyl which may be substituted by halogen, cyano, nitro or C1-C2-alkoxy; n is 0 or an integer from 1 to 4; R is as defined in the description; X is SOm—Rx, NRxRy or NRx—(C═O)—Ry; m is 0 or an integer from 1 to 3; and processes for preparing these compounds, compositions comprising them and their use for controlling harmful fungi are described.