Biological life is an evolving complex dissipative structure, in the sense introduced by Prigogine. The question is considered how life in an advanced stage of evolution manifests itself to an outside observer. Fundamental uncertainties are inherent to the process of self-organization as manifested by dissipative structures. Their evolution is determined by stochastic fluctuations in far from equilibrium conditions, where instabilities arise that cause bifurcations in the behavior of the process system. Since no specific physical or chemical properties of extraterrestrial life can be predicted, general characteristics based on fundamental thermodynamic principles should guide us in our SETI programs. A biological system necessarily must be macroscopic, open with regard of the rest of the universe, and far from thermodynamic equilibrium. The processes within the system must be strongly nonlinear. We should therefore look for life in environments that are in a staticnary far from equilibrium state, such as planetary surfaces and cool interstellar molecular clouds, where an extreme nonequilibrium exists between radiation and kinetic temperature. In any case an advanced form of life should manifest itself by a large entropy emission, possibly carried by low-grade energy radiation, and propably not by information-rich communication channels intended for internal process regulation.