Tough hydrogels can be synthesized by incorporating self-healing physical crosslinks in a chemically crosslinked gel network. Due to the breaking and reattachment of these physical crosslinks, these gels exhibit a rate-dependent behavior that can be different from a classical linear viscoelastic solid. In this work, we develop a theory to describe the linear mechanical response of a dual-crosslink gel in a parallel-plate torsional rheometer. Our theory is based on a newly developed finite strain constitutive model. We show that some of the parameters in the constitutive model can be determined by carrying oscillatory torsional experiments. For consistency, we also show that the torsion data in an oscillatory test can be predicted using our theory with parameters obtained from tension tests. Our theory provides a basis for interpreting and understanding the test data of these gels obtained from rheometry. (C) 2015 The Society of Rheology.