Disclosed are conjugates exhibiting VLA-4 antagonistic properties. Certain of these conjugates also inhibit leukocyte adhesion and, in particular, leukocyte adhesion mediated by VLA-4. The conjugates of this invention are characterized as containing more than one VLA-4 inhibiting compound covalently attached to a bio-compatible polymer, such as polyethylene glycol. Conjugates of the invention are defined by formula I, wherein A, B, and q are described in the specification. Such conjugates are useful in the treatment of inflammatory diseases in a mammalian patient, e.g., human, such as asthma, Alzheimer's disease, atherosclerosis, AIDS dementia, diabetes, inflammatory bowel disease, rheumatoid arthritis, tissue transplantation, tumor metastasis, and myocardial ischemia. The conjugates can also be administered for the treatment of inflammatory brain diseases such as multiple sclerosis.