The talk will address the problem of local limit theorem for dependent structures. A local limit theorem is a fine scale behavior of the sums \$S_n\$ dealing with the rate of convergence of the probability that a partial sum lies in an interval. This type of limit theorem is a fine scale behavior of the sums \$S_n\$. Controlling such probabilities is important for finding recurrence conditions for a random walk. The first class considered is the linear fields of random variables constructed from independent and identically distributed innovations with finite second moment. Then, we consider the local limit theorem for additive functionals of a nonstationary Markov chain with infinite or finite second moment. The method of proof is based on the characteristic function factorization