When a nematic liquid crystal is subject to deformational flow, rotational torques arising from the Leslie viscosities lead to director realignment. In the case when a magnetic field is present these torques compete with the alignment torque associated with magnetic anisotropy. Under purely extensional flow, this competition results in a sudden director flip at a critical rate of strain given by epsilon(c) = chi(a)B(0)(2)/(mu(0)\a(3)+a(2)\), where chi(a) is the anisotropy of the magnetic susceptibility per unit volume of the liquid crystalline polymer, and alpha(2) and alpha(3) are viscosity 6oefficients arising from the anisotropic (or viscous) part of the stress tensor in the Leslie-Ericksen velocity equation. Using a four-roll mill placed in the 7 T magnet of a nuclear, magnetic resonance (NMR) spectrometer, we have observed the orientation of the director, as a function of strain rate, for a flow aligning liquid crystalline polymer consisting of a polysiloxane backbone and mesogenic 4-methoxyphenyl-4'-butenyloxybenzoate side chains,, the temperature being 348 K, just a few degrees below the nematic to isotropic transition. Director orientations were obtained using H-2 NMR spectral splittings from a probe molecule species comprising < 10% methyl-(sulfoxide)-d(6). A distinct director flip is observed at a value of strain rate measured by NMR velocimetry to be 0.037 s(-1). From this value we determine \alpha(2)+ alpha(3)\/chi(a) similar to 107 < 10(7). Pa s. (C) 2004 The Society of Rheology.