In the present paper, an application of recursive parameter identification algorithms to the problem of diagnosing the technological process progress of a nuclear power reactor as a constituent part of the decision support system of nuclear power plant operative personnel. The diagnostics technique applied in the present paper is based on utilizing current estimates of parameters involved in the reactor point kinetic model and characterizing the magnitude of the reactivity being one of the most important dynamic nuclear power reactor characteristics. For the estimation procedure, a recursive parameter identification algorithm is proposed, which does not involve the identification criterion Hessian inversion and preserves the performance stability under closeness of the Hessian to the degeneracy.