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A time-varying distributed H system (TVDH system) is a splicing system which has the following feature: at different moments one uses different sets of splicing rules (these sets are called components of TVDH system). The number of components is called the degree of the TVDH system. The passage from a component to another one is specified in a cycle. It was proved by the first two authors (2001) that TVDH systems of degree one generate all recursively enumerable languages. The proof was made by a sequential modelling of Turing machines. This solution is not a fully parallel one. A. P驴un (1999) presented a complete parallel solution for TVDH systems of degree four by modelling type-0 formal grammars. His result was improved by the first two authors by reducing the number of components of such TVDH systems down to three (2000). In this paper we improve the last result by reducing the number of components of such TVDH systems down to two. This question remains open for one component, i.e. is it possible to construct TVDH systems of degree one which completely uses the parallel nature of molecular computations based on splicing operations (say model type-0 formal grammars).