5-Phenylpyrimidines of the formula I in which the substituents and the index are as defined below: R1,R2 are hydrogen, alkyl, haloalkyl, cycloalkyl, halocycloalkyl, alkenyl, haloalkenyl, alkynyl or haloalkynyl, and R1 and R2 together with the nitrogen atom to which they are attached may also form a saturated or unsaturated ring which may be interrupted by an ether, thio, sulfoxyl or sulfonyl group and may be substituted by one to four groups Ra and/or Rb; R3 is hydrogen, halogen, cyano, alkyl, haloalkyl, alkoxy, haloalkoxy or alkenyloxy; R4 is hydrogen, halogen, cyano, hydroxyl, mercapto, azido, alkyl, alkenyl, alkynyl, haloalkyl, alkoxy, alkenyloxy, alkynyloxy, haloalkoxy, alkylthio, alkenylthio, alkynylthio, haloalkylthio, —ON═CRaRb, —CRc═NORa, —NRcN═CRaRb, —NRaRb, —NRcNRaRb, —NORa, —NRcC(═NRc′)NRaRb, —NRcC(═O)NRaRb, —NRaC(═O)Rc, —NRaC(═NORc)Rc′, —OC(═O)Rc, —C(═NORc)NRaRb, —CRc(═NNRaRb), —C (═O)NRaRb or —C(═O)Rc; in which Ra, Rb and Rc are as defined in the description; X is halogen, alkyl, alkoxy or haloalkyl; and m is an integer from 1 to 5 ; processes for preparing these compounds, compositions comprising them and their use for controlling harmful fungi are described.