Humans utilise multiple communication channels in their social interactions and also information diffusion as well as the spread of influence are practically related with many contexts. Each such context (channel) may represent a different communication method or a different environment of a given person. This facilitates building multiple social networks, that are not independent. They share the same set of nodes connected with many links grounded on different layersthese networks are called

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... lti-layered or multiplex social networks. The influence process may vary in these kinds of social networks depending on the network model, the level of influence for each layer and other factors such as the overlap of nodes and links across layers. In this paper, the influence processes in multi-layered social networks have been analysed showing that for almost all analysed network models, the success in convincing few more individuals may be crucial for the whole influence process. The results revealed that the process is not linear in terms of relation between the number of initially influenced individuals and the total number of influenced nodes. The linear threshold model has been utilized as a base influence model. Keywords-social network analysis; multi-layered networks; multiplex networks; spread of influence; linear threshold I.