Novel methods of synthesizing multiple copies of a target nucleic acid sequence which are autocatalytic are disclosed (i.e., able to cycle automatically without the need to modify reaction conditions such as temperature, pH, or ionic strength and using the product of one cycle in the next one). In particular, methods of nucleic acid amplification are disclosed which are robust and efficient, while reducing the appearance of side-products. In general, the methods use priming oligonucleotides that target only one sense of a target nucleic acid, a promoter oligonucleotide modified to prevent polymerase extension from its 3'-terminus and, optionally, a means for terminating a primer extension reaction, to amplify RNA or DNA molecules in vitro, while reducing or substantially eliminating the formation of side-pro ducts. The disclosed methods minimizes or substantially eliminate the emergence of side-products, thus providing a high level of specificity. Furthermore, the appearance of side-products can complicate the analysis of the amplification reaction by various molecular detection techniques. The disclosed methods minimize or substantially eliminate this problem, thus providing enhanced levels of sensitivity.