The present invention is directed to novel methods of synthesizing multiple copies of a target nucleic acid sequence which are autocatalytic (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, the present invention discloses a method of nucleic acid amplification which is robust and efficient, while reducing the appearance of side products. The method uses only one primer, the "priming oligonucleotide," a 3'blocked promoter oligonucleotide and optionally, a means for terminating a primer extension reaction, to amplify RNA or DNA molecules in vitro, while reducing or eliminating the formation of side products. The method of the present invention minimizes or eliminates 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 present invention minimizes or eliminates this problem, thus providing an enhanced level of sensitivity.