Scaling exponents of the longitudinal and transversal velocity structure functions in numerical Navier¿Stokes turbulence simulations with Taylor¿Reynolds numbers up to Relambda = 110 are determined by the extended self similarity method. We find significant differences in the degree of intermittency: For the sixth moments the scaling corrections to the classical Kolmogorov expectations are delta xi<sub>6</sub><sup>L</sup> = ¿0.21 ± 0.01 and delta xi<sub>6</sub><sup>T</sup> = ¿0.43 ± 0.01, respectively, independent of Relambda. Also the generalized extended self similarity exponents rhop,q = delta xip/delta xiq differ significantly for the longitudinal and transversal structure functions. Within the She¿Leveque model this means that longitudinal and transversal fluctuations obey different types of hierarchies of the moments. Moreover, the She¿Leveque model hierarchy parameters betaL and betaT show small but significant dependences on the order of the moment.