A composition comprising a covalent conjugate between a functional, native hemoglobin molecule and at least one molecule of poly(ethylene glycol), said composition comprising: a. a water-soluble hemoglobin fraction comprising a group of hemoglobin molecules wherein each member of said group of hemoglobin molecules; i. is covalently conjugated to at least one molecule of said poly(ethylene glycol) through an amine moiety of an amino acid residue (e.g., an ε-amine moiety of a lysine residue); ii. is free of chemical cross-linking agents; and iii. has a P 50 of from 9 mm Hg to 14 mm Hg; and b. a water-soluble stabilizer fraction rendering said group of hemoglobin molecules oxidation resistant, said fraction comprising, a stabilizing agent comprising a structural element more reactive with oxygen than said group of hemoglobin molecules; and c. a diluent fraction comprising, a pharmaceutically acceptable diluent in which said hemoglobin fraction is soluble, said composition being free of viral activity, and stably comprising less than 5% methemoglobin; said composition prepared by a method comprising: i. submitting a solution of deoxygenated hemoglobin and a stabilizing agent to a thermal viral inactivation process comprising, exposing said solution to a temperature elevated sufficiently to inactivate all viral activity in said solution (e.g., 60 °C), said exposing being for a time sufficient to achieve said inactivation of all viral activity in said solution (e.g., 10 hours), said stabilizing agent comprising a structural element more reactive with oxygen than said deoxygenated hemoglobin in said solution, thereby minimizing oxygen binding by said deoxygenated hemoglobin, said solution comprising an amount of said stabilizing agent sufficient to prevent formation of more than 5% methemoglobin in said thermal viral deactivation process; and then reoxygenating said deoxygenated hemoglobin to form a reoxygenated virally inactivated hemoglobin solution; and ii. contacting said reoxygenated virally inactivated hemoglobin solution of step (i) with an activated poly(ethylene glycol) molecule of reactivity complementary to an amino acid residue of said hemoglobin, thereby forming a covalent conjugate between poly(ethylene glycol) and hemoglobin molecules in said solution. a. a water-soluble hemoglobin fraction comprising a group of hemoglobin molecules wherein each member of said group of hemoglobin molecules; i. is covalently conjugated to at least one molecule of said poly(ethylene glycol) through an amine moiety of an amino acid residue (e.g., an ε-amine moiety of a lysine residue); ii. is free of chemical cross-linking agents; and iii. has a P 50 of from 9 mm Hg to 14 mm Hg; and i. is covalently conjugated to at least one molecule of said poly(ethylene glycol) through an amine moiety of an amino acid residue (e.g., an ε-amine moiety of a lysine residue); ii. is free of chemical cross-linking agents; and iii. has a P 50 of from 9 mm Hg to 14 mm Hg; and b. a water-soluble stabilizer fraction rendering said group of hemoglobin molecules oxidation resistant, said fraction comprising, a stabilizing agent comprising a structural element more reactive with oxygen than said group of hemoglobin molecules; and c. a diluent fraction comprising, a pharmaceutically acceptable diluent in which said hemoglobin fraction is soluble, said composition being free of viral activity, and stably comprising less than 5% methemoglobin; i. submitting a solution of deoxygenated hemoglobin and a stabilizing agent to a thermal viral inactivation process comprising, exposing said solution to a temperature elevated sufficiently to inactivate all viral activity in said solution (e.g., 60 °C), said exposing being for a time sufficient to achieve said inactivation of all viral activity in said solution (e.g., 10 hours), said stabilizing agent comprising a structural element more reactive with oxygen than said deoxygenated hemoglobin in said solution, thereby minimizing oxygen binding by said deoxygenated hemoglobin, said solution comprising an amount of said stabilizing agent sufficient to prevent formation of more than 5% methemoglobin in said thermal viral deactivation process; and then reoxygenating said deoxygenated hemoglobin to form a reoxygenated virally inactivated hemoglobin solution; and said stabilizing agent comprising a structural element more reactive with oxygen than said deoxygenated hemoglobin in said solution, thereby minimizing oxygen binding by said deoxygenated hemoglobin, said solution comprising an amount of said stabilizing agent sufficient to prevent formation of more than 5% methemoglobin in said thermal viral deactivation process; and then reoxygenating said deoxygenated hemoglobin to form a reoxygenated virally inactivated hemoglobin solution; and ii. contacting said reoxygenated virally inactivated hemoglobin solution of step (i) with an activated poly(ethylene glycol) molecule of reactivity complementary to an amino acid residue of said hemoglobin, thereby forming a covalent conjugate between poly(ethylene glycol) and hemoglobin molecules in said solution.