A gas-permeable material with excellent compatibility with blood comprising polyurethane, polyurethaneurea, or the derivatives thereof is provided. The polyurethane or polyurethaneurea is obtained from a composition that comprises diisocyanate; polysiloxane containing terminal hydroxyl groups; and polyol or polyamine containing at least one tertiary amino gorup. The derivatives of the polyurethane or polyurethaneurea is obtained by the following steps of: converting the tertiary amino groups contained in the polyurethane or the polyurethaneurea to quarternary ammonium groups, and treating the polyurethane or the polyurethaneurea having quarternary ammonium groups with heparin.