The Green-Kubo method for calculating viscosities at zero-shear rate of liquid alkanes by means of molecular dynamics (MD) has been applied. Within this thesis, the common study of simulating viscosities close to ambient pressure has been extended to pressures relevant for studies of elastohydrodynamic lubrication (0.1 to 1000MPa). Furthermore, attempts have been made to elucidate the influence of the chemical structure on the high-pressure rheology of \textit The equilibration of investigated MD systems has been traced by using the Hellinger metric for the time-dependent density distribution function for the one third of the sum of the off-diagonal pressure tensor components. In order to elucidate the influence of the chemical structure, rotational relaxation times were calculated by autocorrelating normalized intramolecular positions and fitting them to an exponentially decaying model. In addition, the partial contributions to the overall pressure tensor used for calculating the viscosity were examined separately to provide further information about the structural influence. It was found that MD results obtained for normal alkanes are in good agreement with experimental measurements, while viscosities of branched alkanes are systematically overestimated. Furthermore, the pressure dependence of the calculated zero-shear viscosities is well described by Roelands' pressure viscosity relation. Analysis of different contributions to the pressure tensor showed that in contrast to the normal alkanes, the pressure tensor contribution due to bonds dominates over the angle contributions in branched alkanes. Finally, it was also found that when the Green-Kubo method is applied to systems with long relaxation times, significant computational efforts are necessary to obtain statistically reliable results.