High-throughput sequencing of transcriptomes (RNA-Seq) has recently become a powerful tool for the study of gene expression. We present rSeqDiff, an efficient algorithm for the detection of differential expression and differential splicing of genes from RNA-Seq experiments across multiple conditions. Unlike existing approaches which detect differential expression of transcripts, our approach considers three cases for each gene: 1) no differential expression, 2) differential expression without differential splicing and 3) differential splicing. We specify statistical models characterizing each of these three cases and use hierarchical likelihood ratio test for model selection. Simulation studies show that our approach achieves good power for detecting differentially expressed or differentially spliced genes. Comparisons with competing methods on two real RNA-Seq datasets demonstrate that our approach provides accurate estimates of isoform abundances and biological meaningful rankings of differentially spliced genes. The proposed approach is implemented as an R package named rSeqDiff.