This paper gives the results of a study of the nonlinear viscoelastic behavior of three heavy crude oils from California and Venezuela. A linear combination of normal stress coefficients at zero shear is expressed in terms of the quantity (the climbing constant) used to measure the height rise on a rotating rod. Measurements of the climbing constants are given for the crude oils. Values of both the first and second normal stress coefficients at zero shear are determined by the climbing constant when another combination of the two coefficients is known. In principle, the required information can be obtained by back extrapolation of the first normal stress difference, by back extrapolation of the dynamic modulus or by back extrapolation of the ratio of the second to first normal stress difference. Back extrapolation of data can be achieved when measurements are available at shear rates low enough to enter onto the second-order plateau of the functions generated by different instruments. Examination of previously published data for well-characterized solutions suggests that second-order rheology is most readily obtained in rod climbing.