Pharmaceutical compositions and methods of inhibiting the enzyme elastase and increasing the biological half-life and/or potency in terms of inhibitory activity of the enzyme elastase of peptide compounds is achieved by use of a polymer of the formula P--(L--R)q wherein P is a polymer containing at least one unit of the formula (An Bn) wherein An Bn is substantially nonbiodegradable, and has an average molecular weight of about 1,000 to 5,000 daltons, L is a covalent bond or a linker group and R is a peptide
