The present invention relates to novel modified proteins having N-terminal free thiols that can be produced by recombinant methods and are ready for further chemical derivatization. In particular, the invention relates to erythropoietin conjugate compounds having altered biochemical, physiochemical and pharmacokinetic properties. More particularly, one embodiment of the invention relates to erythropoietin conjugate compounds of the formula: (M)n-X-A-cys-EPO   (I) where EPO is an erythropoeitin moiety selected from erythropoietin or an erythropoietin variant having at least one amino acid different from the wild-type human EPO, or any pharmaceutical acceptable derivatives thereof having biological properties of causing bone marrow cells to increase production of red blood cells; cys represents the amino acid cysteine and occurs at position -1 relative to the amino acid sequence of the erythropoietin moiety; A indicates the structure of the residual moiety used to chemically attach X to the thiol group of -1Cys; X is a water soluble polymer such as a polyalkylene glycol or other polymer; M is an organic molecule (including peptides and proteins) that increases the circulating half-life of the construct; and N is an integer from 0 to 15.