The paper discusses selected postformal concepts of intelligence. They constitute a specific extension of Piaget's theory to include the stage of operations built upon formal operations structures. Researchers have proposed various characteristics of operations formed 'beyond formal operations'. Depending on the recognized features of reasoning revealed within the process of solving the everyday pragmatic problems, the following are distinguished: relativistic operations (J. D. Sinnot), dialectical operations (M. Bassechese), systematic, meta-systematic and paradigmatic operations (Commons, Richards), inter-systematic and inter-subjective operations (G. Labouvie-Vief). The application of these operations provides the individual with a new cognitive ability, defined by Arlin as problem finding ability, in addition to problem solving. On the example of the description of post-formal operations as proposed by Labouvie-Vief, the paper attempts answering the question whether these operations open a new stage in intelligence development.