Selecting animals for their resistance to diseases is a way to improve their health and welfare and reduces the need for veterinary treatment. The objectives of this study were to estimate: i) the genetic parameters for simple visually assessed disease syndromes, and for a composite trait of resistance to infectious disease including all disease syndromes, ii) their genetic correlations with production traits. Clinical signs were recorded during weighing at 63 or 70 days of age on above 150,000 rabbits of two commercial paternal rabbit lines (HYPLUS) of the French breeding company Hypharm. Disease traits were: digestive syndromes, respiratory syndromes, infectious syndromes (a composite trait including digestive and respiratory syndromes), and infectious mortality. The production traits were body weight and carcass yield at 63 or 70 days of age. The heritabilities were low for disease traits (0.01 to 0.08 ± 0.01), and moderate for production traits. The genetic correlations between digestive and respiratory syndromes were slightly negative (-0.18 ± 0.07). The genetic correlations between the composite infectious disease trait and digestive or respiratory syndromes were moderate (0.65 ± 0.04 and 0.61 ± 0.04, respectively). Genetic correlations between disease and production traits were either null or favorable. Our results indicate that it is possible to select rabbits using visually assessed disease syndromes without the need for a trade-off between health and production traits. Using a composite criterion that includes all infectious syndromes is a promising way to improve the general disease resistance in rabbits.