Provided herein are methods for ameliorating an adverse effect of systemic administration of a PEG hyaluronan degrading enzyme to a subject. The methods involve systemically administering a PEGylated hyaluronan degrading enzyme, particularly a PEGylated hyaluronidase, such as any of the animal or bacterial hyaluronidases, to the subject and administering an amount of a corticosteroid sufficient to ameliorate the adverse effect. Also provided are method of treating a hyaluronan-associated disease or condition for single-agent therapy or combination therapy.