In the electric substations, risk-free operation of power transformers is important, as unexpected failures and outage can result in serious accidents and lead to high costs that are undesirable in an increasingly competitive environment. The loss of the mechanical strength and the aging of oil-impregnated cellulose insulation are important factors which limit the operating life of transformers. There is a constant concern for the determination of new chemical markers and methods for identifying cellulose insulation degradation in transformers as early as possible. This paper presents the determination of the state of degradation of solid insulation in a transformer based on 2-furfuraldehyde (2-FAL) and methanol (MeOH) chemical markers by using a system based on neural networks with a Bayesian-type training algorithm.