A method is described for the direct, exponential amplification and sequencing ("DEXAS") of a DNA molecule from a complex mixture of nucleic acids, wherein truncated DNA molecules as well as DNA molecules of full length are synthesized simultaneously and exponentially between two positions on the said DNA molecule, which initially contains a DNA molecule in a thermocycling reaction, a first primer, a second primer, a reaction buffer, a thermostable DNA polymerase, a thermostable pyrophosphatase (optionally), deoxynucleotides or derivatives thereof and a dideoxynucleotide or derivatives thereof. In a preferred embodiment of the method of the invention, direct sequencing of RNA can be performed using one polymerase having a Tabor-Richardson mutation, or a functional derivative thereof, and reverse transcriptase activity. In a more preferred embodiment of the method of the invention, direct sequencing of RNA can be performed in one step, in one vessel.