We describe some aspects of complex behaviour that can be present in biopolymers. The study is based on a nonlinear thermodynamics of non-equilibrium, dissipative systems. Such complexity consists of a Frohlich- Bose- Einstein-like condensation and propagation of Schrodinger- Davydov soliton-wave-like excitations, which are of relevance in Bioenergetics. The question of the soliton lifetime under physiological conditions is discussed, and comparison made with experiments performed in the case of an organic molecular polymer. Further complex behaviour apparently present in ultrasonic medical imaging, dubbed the Frohlich- Cherenkov effect, is briefly discussed.