For human mammary and ovarian carcinomas and transplantation tumours of rats clear hints found for an enzymatic-lytic effects of infiltrating tumour cells as a premise of the invasive tumour growth. In contrast in malignant melanomas there is no functional sign for a specific enzymatic-lytic effect of the living tumour cells to the surrounding tissue. In the mamma carinomas and ovarian carcinomas infiltratively growing tumour districts were characterized by an increased activity of the NADH-D, LDH, G-6-P-DH, IDH, MDH, SPase, UE, LAP and beta-GD. The transplantation tumours showed a high number of tumour cells with a high leucine amino-peptidase- and beta-glucuronidase-activity in a middle zone that was localized under the tumour edge district. The increased activity of the LAP and beta-GD found in the infiltration zone of the tumours is considered as an demonstration of a strong proteolytic activity of the tumour cells. The findings are discussed in the aspect of the invasive tumour growth.