The means of operational checking used for modern network computer systems need to check their behavioral properties, which is reflected in the construction and application of developed scenarios for distributed background checking of the functioning of networked computer systems (NCS) and their components. The purpose of this paper is to increase the completeness of the behavioral operational checking performed for the NCS components in real time, the main function taking into account the time and random characteristics of the work. This possibility can be obtained by presenting components of NCS with extended Petri nets. To achieve the goal, the following tasks are solved: constructing a behavioral operational checking model for the NCS component based on the recognition of Petri net functions; definition of the main steps of the procedure for performing behavioral operational checking of NCS components; Estimating the expected computational complexity of the received behavioral operational checking. The model of behavioral operational checking presented in this work is based on the organization of a background recognition experiment for an extended Petri net. The expanded Petri net introduces interval (time) and probabilistic properties of functions for positions and transitions. The model has the features of recognition of the advanced functions of the Petri net, the use of behavior identifiers, checking primitives and fragments based on them, as well as the signature of the fragments composition operations and relations for them. Preliminary construction of identifiers can be performed on the basis of special graphs of achievable markings. Identifiers and primitives along with the operations of transforming the behavior of the Petri net into its recognized structure make it possible to construct a procedure for comparing the behavior of the tested and reference component in the course of operational checking. The model and procedure can be taken as a basis for determining the conditions of behavioral operational checking, building a distributed method and a operational checking system of NCS. General analytical estimates of the dimension of the length of the checking analysis show its attainability with the use of modern means of operational checking.