Аннотация:В статье приводятся новые уточненные оценки скорости сходимости в локальных предельных теоремах для плотностей сумм независимых одинаково распределенных случайных величин.New non-uniform estimates of the accuracy of the normal approximation for the densities of sums of independent identically distributed random summands are proved. These estimates are used for the construction of the estimates in Lp-metric. As a corollary, a refined estimate is obtained of the accuracy of the normal approximation for the distribution functions of sums of independent identically distributed random summands.