This paper describes tension-torsion multiaxial creep-fatigue for CMSX-2 nickel base single crystal superalloy at 1173K. Strain controlled tension-torsion low cycle fatigue tests with hold-times were carried out using hollow cylinder specimens, of which the axis agrees with [001] crystallographic direction. Hold-times in torsion tests were more detrimental to lifetimes than those in tension tests. Mises' equivalent strain range parameter gave a large scatter for the correlation of creep-fatigue lives. The relationship between creep-fatigue lifetime and elastic strain range had strong dependence on a principal strain ratio but that between the lifetime and plastic and creep strains had almost no dependence. A linear damage rule gave a proper estimate in tension tests, but substantially overestimated lifetimes in torsion tests. A new simple lifetime prediction method, taking account of anisotropy of the elastic modulus, was proposed. The method predicted the experimental lifetimes within a factor of 3 scatter band. Cracks in tension tests propagated in a principal strain direction but these in torsion tests in a maximum shear direction. In torsion tests, cracks were only observed in soft-zones predicted by numerical analyses.