The paper presents preliminary results related to the logical analysis of the concept of infallibility. The concept is explicated using the resources of modal logic, namely in terms of the operator of possibility M and the operator of belief B. Infallibility with respect to p is explicated as impossibility of being wrong with respect to p. The infallibility operator is introduced: Iϕ is defined to mean the same as ¬M(Bϕ ∧ ¬ϕ). We prove various theorems about validity or invalidity of certain formulas with I in special classes of models for the combined language.