The main notion and the stem of the theory of optimum planning the search for a space object (SO) by the incomplete orbital information on it is the principle of equivalence of the search plan elements for different times. So far the theory as well as the equivalence principle were developed constructively (up to the real search methods and working programs) for the important case of taking into account the initial state vector error only along the track. For this case practical application of the equivalence principle appeared to be very convenient which makes the search planning procedure practically simple enough. But except this case there exist many search situations where one cannot neglect the state vector errors in different directions. For such situations the equivalence principle as the main tool of optimum planning the search for a SO should be generalized to the majorizing equivalence principle. After a short reminder of the former formulation of the principle its new generalization is introduced. The theoretical account is accompanied by some elucidating examples. The generalized equivalence principle can be used for practical constructing optimum plans of search for SOs by rough a priori orbital information in the most common case of the state vector errors.