The invention relates to Agrobacterium mediated transformation of moulds comprising species of the fungal sub-divisions Ascomycotina, Basidiomycotina, Deuteromycotina, Mastigomycotina, and Zygomycotina. Examples demonstrate the transformation of Aspergillus awamori (both protoplasts and conidia), Aspergillus nidulans, Aspergillus niger, Colletotrichum gloeosporioides, Fusarium solani pisi, Neurospora crassa, Trichoderma reesei, Pleurotus ostreatus and Agaricus bisporus (all conidia), and Fusarium graminearum (both conidia and rehydrated freeze dried ATCC material). Especially for Aspergillus awamori the transformation frequency is much higher than with conventional mould transformation techniques. It has further been found that not only one expressable gene can be introduced into these moulds, but even multiple copies of such gene, which, moreover, can be targeted e.g. in the chromosomal pyrG locus, as exemplified for A. awamori. These multiple copies can be of a gene encoding a desired, homologous or heterologous, protein.