The invention relates to aryl alkanoylpyridazine derivatives of the formula (I) and their physiologically compatible salts and solvates, where R1, R2, Q and B have the meanings given in claim 1. Said compounds have a phosphodiesterase-IV inhibiting action and can be used in the treatment of allergic disorders, asthma, chronic bronchitis, atopic dermatitis, psoriasis and other skin diseases, inflammatory diseases, auto-immune diseases such as rheumatoid arthritis, multiple sclerosis, Crohn's disease, diabetes mellitus or ulcerative colitis, osteoporosis, transplant rejection reactions, cachexia, tumour growth or tumour metastases, sepsis, memory disturbances, atherosclerosis and AIDS.