I would like to present fruitful results of the authors, i.e. completely new approach, that makes the method of thermodynamical formalism available for a wide class of meromorphic funcions of finite order. I will show how to associate to a given meromorphic function a suitable metric, and then use Nevanlinna's theory to construct conformal measures with respect to the new metric. Finally, I will list some nice properties of Gibbs states, obtained in this paper.