The one-dimensional coordination polymer catena-poly[diaqua(sulfato-κO)copper(II)]-μ2-glycine-κ(2)O:O'], [Cu(SO4)(C2H5NO2)(H2O)2]n, (I), was synthesized by slow evaporation under vacuum of a saturated aqueous equimolar mixture of copper(II) sulfate and glycine. On heating the same blue crystal of this complex to 435 K in an oven, its aspect changed to a very pale blue and crystal structure analysis indicated that it had transformed into the two-dimensional coordination polymer poly[(μ2-glycine-κ(2)O:O')(μ4-sulfato-κ(4)O:O':O'':O'')copper(II)], [Cu(SO4)(C2H5NO2)]n, (II). In (I), the Cu(II) cation has a pentacoordinate square-pyramidal coordination environment. It is coordinated by two water molecules and two O atoms of bridging glycine carboxylate groups in the basal plane, and by a sulfate O atom in the apical position. In complex (II), the Cu(II) cation has an octahedral coordination environment. It is coordinated by four sulfate O atoms, one of which bridges two Cu(II) cations, and two O atoms of bridging glycine carboxylate groups. In the crystal structure of (I), the one-dimensional polymers, extending along [001], are linked via N-H···O, O-H···O and bifurcated N-H···O,O hydrogen bonds, forming a three-dimensional framework. In the crystal structure of (II), the two-dimensional networks are linked via bifurcated N-H···O,O hydrogen bonds involving the sulfate O atoms, forming a three-dimensional framework. In the crystal structures of both compounds, there are C-H···O hydrogen bonds present, which reinforce the three-dimensional frameworks.