Classical views of hereditary mechanisms consider linear nucleic acids, DNA and RNA, as template molecules wherein genetic information is encoded by the sequence of nitrogenous bases. The template principle embodied in the central dogma of molecular biology describes the allowed paths of genetic information transfer from nucleic acids to proteins. The discovery of prions revealed an additional hereditary mechanism whereby the spatial structure is transmitted from one protein molecule to another independently of the sequence of nitrogenous bases in their structural genes. The simultaneous existence of linear (type I) and conformational (type II) templates in one cell inevitably implies their interaction. The review analyzes the current data confirming the idea that protein amyloid transformation may influence the genome stability and considers potential mechanisms of interactions between type I and type II template processes. Special attention is paid to the joint contribution of the two process to tumor "evolution" and the mechanisms of genome destabilization due to amyloid transformation of proteins in Alzheimer's and Parkinson's diseases and Down syndrome.