We present results from a comprehensive investigation of the rheological responses of the gelled waxy crude oils during the yielding transition process by both stress-controlled and strain-controlled tests. If the deformation is within the linear viscoelastic region, G' increases slowly with increasing frequency following a power-law relationship. 80% of the total deformation accumulated during creeping is recoverable, and this recoverability remains largely independent of both imposed stress and testing time. The waxy gel relaxes the restored stress slowly with a time scale of similar to 100 s. If the induced deformation exceeds the linear viscoelastic region, the elasticity of waxy structure starts to gradually decay with increasing creep stress and creep time, and the plastic contribution has come into play in the nonlinear region. A rapid reduction in the obtained time scale is observed with increasing applied strain. After the structure fractures, both G' and G'' decrease with increasing strain following a power-law relationship. The ratio of the large amplitude shear-thinning exponents of G' and G'' is around 2, indicating a more rapid decay of the elastic property than the viscous property. A brittleness index I is defined to quantitatively describe the brittleness of the waxy gel. The value of I for the waxy gel formed at lower temperatures is smaller, indicating that the waxy gel tends to have a more brittle fracture when yielding. The values of linear storage modulus G' (gamma(0) -> 0), critical linear strain gamma(1), critical linear stress sigma(1), and yield strain gamma(y) obtained by different rheological testing methods are found to be well consistent. The yielding transition process is found to be strain determined rather than stress determined, and thereby gamma(1) and gamma(y) rather than yield stress are suggested to indicate the yielding transition. (C) 2018 The Society of Rheology.