Alternative splicing, an unknown mechanism 20 years ago, is now recognized as a major mechanism for proteome and transcriptome diversity, particularly in mammals -- some researchers conjecture that up to 90% of human genes are alternatively spliced. Despite much research on exon and intron evolution, little is known about the evolution of transcripts. In this paper, we present a model of transcript evolution and an associated algorithm to reconstruct transcript phylogenies. The evolution of the gene structure -- exonsand introns -- is used as basis for the reconstruction of transcript phylogenies. We apply our model and reconstruction algorithm on two well-studied genes, MAG and PAX6, obtaining results consistent with current knowledge and thereby providing evidence that a phylogenetic analysis of transcripts is feasible and likely to be informative.