among self-replicating molecules, they have to be connected by a positive feedback loop of catalytic actions. This kind of closed network consisting of self-replicating entities connected by a catalytic positive-feedback loop was named an elementary hypercycle. Such a concept, apart from an increased information capacity, has another advantage. Linking self-replication with mutual catalysis can produce nonlinear growth of the system. This, first, makes the system resistant to so-called parasitic branches. Parasitic branches are species coupled to a cycle that do not provide any advantage to the reproduction of a cycle, which, in turn, makes them useless and decreases the selective value of the system. Secondly, it reinforces the self-organization of molecules into the hypercycle, allowing the system to evolve without losing information, which solves the error threshold problem. Analysis of potential molecules that could form the first hypercycles in nature prompted the idea of coupling an information carrier function with enzymatic properties. At the time of the hypercycle theory formulation, enzymatic properties were attributed only to proteins, while nucleic acids were recognized only as carriers of information. This led to the formulation of a more complex model of a hypercycle with translation. The proposed model consists of a number of nucleotide sequences I (I stands for intermediate) and the same number of polypeptide chains E (E stands for enzyme). Sequences I have a limited chain length and carry the information necessary to build catalytic chains E. The sequence Ii provides the matrix to reproduce itself and a matrix to build the protein Ei. The protein Ei gives the catalytic support to build the next sequence in the cycle, Ii+1. The self-replicating sequences I form a cycle consisting of positive and negative strands that periodically reproduce themselves. Therefore, many cycles of the +/− nucleotide collectives are linked together by the second-order cycle of enzymatic properties of E, forming a catalytic hypercycle. Without the secondary loop provided by catalysis, I chains would compete and select against each other instead of cooperating. The reproduction is possible thanks to translation and polymerization functions encoded in I chains. In his principal work, Manfred Eigen stated that the E coded by the I chain can be a specific polymerase or an enhancer (or a silencer) of a more general polymerase acting in favour of formation of the successor of nucleotide chain I. Later, he indicated that a general polymerase leads to the death of the system.