The general aim of this thesis was to study the genetic determinism for some traits related to artificial insemination (AI) dose production of fresh and frozenthawed semen, in order to explore the interest and limitation of different strategies for their genetic improvement in a paternal line of rabbits selected for growth rate during the fattening period (28-63 days).In chapter 1, genetic parameters of sperm production traits are estimated as well as the genetic relationship with daily gain (DG). The heritabilities (h 2 ) of the semen traits were 0.13±0.05, 0.08±0.04 and 0.07±0.03 for ejaculate volume (V), sperm concentration (CN) and sperm production (PROD) per ejaculate, respectively. A favourable and moderate genetic correlation was observed between V and DG (0.36±0.34). From this chapter it may be concluded that if a seminal trait is to be included as a selection objective, a useful one could be sperm production, as it is a trait in which both volume and concentration are included.Moreover, there is currently no evidence to suggest that selection for DG in rabbits will affect sperm production adversely.The aim of chapter 2 was to explore the genetic determinism of some sperm quality traits and their genetic relation with the selection criteria of the paternal rabbit line. The heritabilities (h 2 ) of semen quality traits commonly evaluated in a classic spermiogram were 0.18, 0.19 and 0.12 for NAR (%, percentage of sperm with intact acrosome), ANR (%, percentage of sperm abnormalities) and MOT (%, percentage of total motile sperm cells) respectively. We also estimated the h 2 of some motion CASA parameters 0.09, 0.11, 0.10, 0.11, 0.11 and 0.11 for VAP (µm/s; average path velocity), VSL (µm/s; straight-line velocity), VCL (µm/s; curvilinear velocity), LIN (%, linearity index), ALH (µm; amplitude of the lateral head displacement), STR (%, straightness). Genetic correlations between DG and semen traits showed a high HPD95% (interval of highest density of 95%).However there is some consistent evidence of the negativity of the genetic correlations of DG with NAR and MOT (-0.40 and -0.53, respectively).Chapter 3 aims to determine the repeatability and heritability of sperm head characteristics: width (W, μm), area (A, μm2),length (L, μm) and perimeter (P, μm), and explore the relationships between them and with the selection The environmental and male effects that could have an influence on sperm freezability are studied in Chapter 4. Six different traits were evaluated: sperm concentration (CONC, 10 6 spermatozoa/mL), acrosome integrity in fresh (NAR, %) and frozen-thawed semen (Nar-FT, %), sperm motility in fresh (MOT, %) and frozen-thawed semen (Mot-FT, %) and the percentage of viable sperm in frozen-thawed semen (Live-FT, %). In addition, two synthetic traits were computed: the relative reduction of acrosome integrity (Rnar, %) and relative reduction of motility (Rmot, %) after the freezing-thawing process. A multipletrait recursive model was used to analyse the relationships between the semen traits...