For the genus-specific or/and species-specific detection of bacteria in a sample liquid, bacterial RNA is hybridized with a primer which is complementary to a genus-specific or species-specific region of the RNA of particular bacteria or to a highly conserved region of the RNA of bacteria in general, but which is not complementary at its 3′ end to the RNA of bacteria of another genus or species, the primer is elongated in the presence of a suitable polymerase and the four deoxyribonucleotides, if desired, with a concurrent or subsequent labelling of the elongation product and an elongation product formed is hybridized with a genus-specific or species-specific oligonucleotide after denaturation and the hybridization is detected by means of the oligonucleotide label.