Genetic parameters and genetic trends of total number of born kits (TNB), and number of kits born alive (NBA) were estimated in Pannon White and Pannon Ka rabbits for the first four parities. REML and BLUP procedures were applied using repeatability and multi-trait animal models (PEST and VCE software). Heritability estimates were low for both traits and breeds and ranged between 0.060.43–0.07 (0.010.43–0.02) and 0.040.43–0.06 (0.020.43–0.02) for TNB and NBA, respectively (standard errors of estimates are given in brackets). The estimated permanent environmental effects showed higher relative importance compared to the additive genetic effects and they ranged between 0.070.43–0.13 (0.010.43–0.02) and 0.080.43–0.14 (0.010.43–0.02) for TNB and NBA, respectively. High genetic correlation coefficients were found between TNB and NBA (0.97±0.02, 0.96±0.02) for Pannon White and Pannon Ka, respectively. The genetic correlation coefficients estimated between TNB and between NBA of the successive parities (as separate traits) ranged between 0.640.43–0.97 (0.040.43–0.11) and 0.560.43–0.99 (0.030.43–0.10) for Pannon White and Pannon Ka, respectively. The estimated genetic trends for TNB and NBA were negligible for the Pannon White and small (0.030.43–0.02 [0.010.43–0.01]) for Pannon Ka. The mean squared errors (MSE) of the repeatability and multi-trait models were similar but the correlation coefficients of between the observed and predicted values were lower for the multi-trait (0.270.43–0.61) than for the repeatability models (0.43–0.65).