The present invention is directed to a simple process for the modification of the specificity of a peptidase of the hemostatic system by coupling polymers to the peptidase causing it to lose its reactivity in the hemostatic system, but enabling it to continue to react with certain inhibitors, effectors and substrates. The invention is furthermore directed to processes for the detection or quantitative determination of inhibitors of the peptidase in bodily fluids or other samples as well as to processes for their neutralization and/or removal from liquids. Finally, the invention allows the use of a polymer-coupled peptidase as drug and furthermore provides a device which makes use of such a peptidase in the removal of peptidase inhibitors from samples or from the bloodstream of a patient.