This paper presents a technique for the efficient compression of high dynamic range video (HDR) sequences. Such video sequences usually represent several orders of magnitude of real-world luminance intensity levels. Therefore, they are mostly stored in a floating-point represention. In order to obtain a coded representation that is bit stream compatible with the H.264/AVC video coding standard, the float-valued HDR values have to be mapped to a suitable integer representation first. The mapping proposed in this paper is adapted to the dynamic range of each video frame. Furthermore, to compensate for the associated dynamic contrast variation across frames, a weighted prediction method and quantization adaptation are introduced. The experiments show that the proposed method offers highly efficient HDR video compression. Only a fraction of the bit rate of a non-adaptive reference method is required to represent an HDR video sequence at the same quality.