This invention describes the new 6-alkenyl- and 6-alkinyl-epothilone derivatives of general formula (I) in which R1a, R1b, R2b, R3a, R3b, R4, R5, R6, R7, A, Y, D, E, G, Y and Z have the meanings that are indicated in the description. The new compounds interact with tubulin by stabilizing microtubuli that are formed. They are able to influence the cell-splitting in a phase-specific manner and thus find use in treating diseases or conditions associated with the need for cell growth, division and/or proliferation. Thus the compounds are suitable for treating malignant tumors, for example, ovarian, stomach, colon, adeno-, breast, lung, head and neck carcinomas, malignant melanoma, acute lymphocytic and myelocytic leukemia. In addition, they are suitable for anti-angiogenesis therapy as well as for treatment of chronic inflammatory diseases (such as psoriasis, arthritis). Methods of use and preparation of the compounds are also described.