Self-assembly of DNA is considered a fundamental operation in realization of molecular logic circuits. We propose a new approach to implementation of data flow logical operations based on manipulating DNA strands. In our method the logic gates, input, and output signals are represented by DNA molecules. Each logical operation is carried out as soon as the operands are ready. This technique employs standard operations of genetic engineering including radioactive labeling as well as digestion by the second class restriction nuclease and polymerase chain reaction (PCR). To check practical utility of the method a series of genetic engineering experiments have been performed. The obtained information confirms interesting properties of the DNA-based molecular data flow logic gates. Some experimental results demonstrating implementation of a single logic NAND gate and only in one vessel calculation of a tree-like Boolean function with the help of the PCR are provided. These techniques may be utilized in massively parallel computers and on DNA chips.