In this paper, Laplace approximation formula is efficiently used to calculate infinite-series expression for average level crossing rate (LCR) of the product of Nakagami-m and kappa-mu random processes. The results can be used in performance analysis of dual-hop relay wireless mobile communication system in specific multipath fading environment when the first section is under the influence of NLOS multipath environment while the second section is under the influence of LOS multipath fading environment. The influences of multipath fading parameters on the LCR of the proposed model are examined, graphically presented and discussed. Moreover, analytical approach of applying Laplace approximation formula in multi-hop systems is further considered by obtaining closed form expressions for the LCR of the product of three and four Nakagami-m processes, respectively. Key words: average level crossing rate, kappa-mu multipath fading, Laplace approximation formula, Nakagami-m distribution, relay communications system.