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In the paper asymptotic expansions for second-order moments of integral functionals of a family of random processes are considered. The random processes are assumed to be wide-sense stationary and c-correlated, i.e. the values are not correlated excluding an c-neighbourhood of each point. The asymptotic expansions are derived for e -0. Using a special weak assumption there are found easier expansions as in the case of general weakly correlated random processes. Expansions are given for integraldoi:10.4171/zaa/949 fatcat:c5xmeozxargdliljzas3acavay