The linewidth and second moment of oriented samples of drawn PE and POM were measured as a function of temperature. from -196° to 160°C, and of the angle between draw direction and magnetic field H0, mostly at 0°, 45°, and 90°. Much detail in the temperature behavior of these quantities is resolved which cannot be observed with unoriented samples. On the basis of linewidth measurements of drawn PE, an interpretation of the high‐temperature narrowing of the broad line observed with PE single crystals and PE crystallized from the melt is given. The anisotropy of the decrease in second moment with rising temperature which is related to anisotropic molecular motion was determined for PE, subtracting the contribution due to lattice expansion from the total decrease measured. The ``mobile fraction'' was determined for the two polymers as a function of temperature. In both cases a reduction of mobile fraction upon drawing is observed.