A cross experiment was carried out in Animal Production Research Institute (APRI), in cooperation with Benha University, Egypt for three years starting from February 2013 and terminated 2016. Four pedigreed local strains of chickens Matrouh (MT), Mandarah (MN), Inshas (IN) and Silver Montazah (SM) strains were used. A total of 34 sires and 230 dams from MN strain, 32 sires and 194 dams from MT strain were chosen randomly from 250 cockers and 600 pullets to produce purebreds and crossbreds progenies in the first generation. In the second generation, the crossbred hens of MNxMT were artificially inseminated with fresh semen of Inshas strain (IN), while the crossbred hens of MTxMN were artificially inseminated with fresh semen collected from cocks of Silver Montazah strain (SM) to produce three-way crossbreds (½IN×¼MN¼MT and ½SM×¼MT¼MN). Single trait animal model was used in estimating heritability and in predicting the breeding values (PBV). Crossbreeding effects of direct additive (G^I), maternal effects (G^M), direct heterosis (H^I) and maternal heterosis (H^I) were estimated using the procedure of generalized least-squares. The overall means of all genetic groups were 154 day, 1420 g, 39.38 g, 45 egg, 1957 g, 61 egg, 2727 g, 16 day, 411 g, 18 egg, 784 g, 13.5 egg and 593 g for ASM, BWSM, WFE, EN90D, EM90D, EN120D, EM120D, PF10E, EMF10E, EN2DW, EM2DW, EN1WM and EM1WM, respectively Estimates of heritability were moderate for ASM and BWSM (0.23 and 0.69), while they were low for egg production and partial egg recording traits. The GLM showed that three-way crossbreds reported the earlier ASM, heavier BWSM and WFE, the highest EN90D, EN120D and EN2DW and the heaviest EM90D, EM120D and EM2DW. The ranges of predicted breeding values (PBV) of MT strain were slightly higher than that for MN birds. Ranges of PBV recorded by ½MT½MN were nearly similar to those ranges recorded by ½MN½MT. Cross fathered by SM cocks and mothered by (½MT½MN) had higher ranges in PBV for egg production and partial egg recording traits than those cross fathered by IN cocks and mothered by (½MN½MT). The effects of G^I on all traits (p≤0.01) and in favour of MN breed. The percentages of G^M were significant for sexual maturity traits and non-significant for egg production and partial egg recording traits. Percentages of H^I (-3.8, 28.5, -4.6, 29.3, 28.8, 24.9, 19.7, -36.1, -3.2, 17.4, 10.6 and 8.8%) and H^M (-2.6, 1.2, 0.03, 7.8, 8.2, 7.8, 8.1, -10.5, 0.2, 7.2, 0.7, 3.2 and 3.3%) were mostly highly significant for all traits for ASM, BWSM, EN90D, EM90D, EN120D, EM120D, PF10E, EMF10E, EN2DW, EM2DW, EN1WM and EM1WM, respectively. We can recommend that Mandarah strain (MN) could be used as a sire and Matrouh (MT) as a dam, depending on the estimates of the direct additive genetic effect G^I for the studied traits which were in favor of MN.