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Limit theorems for the likelihood ratio in the hypotheses testing problems of general binary statistical experiments are considered. Both completely asymptotically distinguishable and contigual families of hypotheses are investigated. The law of large numbers and the large deviation theorems and the theorems of a weak convergence for the logarithm of the likelihood ratio are considered. In the conditions of the validity of these theorems, a behaviour of the 1st and 2nd type error probabilities for the Neyman-Pearson test is studied. The obtained results are applied to particular statistical experiments generated by various stochastic processes.

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