We present a FrameNet-based semantic role labeling system for Swedish text. As training data for the system, we used an annotated corpus that we produced by transferring FrameNet annotation from the English side to the Swedish side in a parallel corpus. In addition, we describe two frame element bracketing algorithms that are suitable when no robust constituent parsers are available. We evaluated the system on a part of the FrameNet example corpus that we translated manually, and obtained an accuracy score of 0.75 on the classification of presegmented frame elements, and precision and recall scores of 0.67 and 0.47 for the complete task.