Properties of the Frőhlich model of collective oscillations of polar molecules (such as proteins) residing inside, or in the plasma membrane, of bio\-logical cells, receiving energy from intracellular metabolic sources and giving it off to surroundings, are studied. The exchange mechanisms with the heat bath can be linear and non-linear. Particular attention is given to condensation of energy in the lowest-frequency (fundamental) mode. Occurrence of this phenomenon, which is of importance for generation of electromagnetic fields by the cells as well as for other functions, presupposes that the non-linear interaction coefficient exceeds certain limit; if it is too small, the incoming energy is distributed to all modes. This can happen e.g. in the context of cancerous conditions due to perturbation of high static electric fields around mitochondria which are necessary support for non-linear behaviour. On the contrary, if interaction with the heat bath is too high, the oscillator system leaks energy to surroundings and must be pumped heavily to attain condensation.