The global stresses in turbostratic and cubic boron nitride films are studied during annealing up to 670 degreesC. Stress relaxation is observed when the deposition temperature is exceeded. The compressive intrinsic stress in both tBN and cBN decreases exponentially with the time constant of 7 - 8 min. Depth-resolved analysis of the stress before and after annealing reveals that the features in the stress depth profile do not smear out during annealing. The stress relaxation in the interfacial turbostratic boron nitride exceeds that in the cubic boron nitride on top by a factor of 1.5 +/- 0.2, and is thus not significantly affected by the capping layer of cubic boron nitride. The specific thermal stresses in turbostratic and cubic boron nitride films are not altered after thermal treatment up to 670 degreesC. It is concluded that the decrease in stress is mainly due to changes in strain, whereas the elastic properties of boron nitride films remain largely constant under annealing.