Introgressive hybridization between genetically divergent populations is an important evolutionary process. The degree to which repeated hybridization events between the same parental taxa lead to similar genomic outcomes is unknown. This study addressed this question by following genomic trajectories of replicate hybrid swarms of the copepod Tigriopus californicus over many generations of free mating. Swarm composition was determined both by differential reproductive success of founder individuals and subsequent selection on hybrid genotypes. For one cross, between two populations showing differential fitness in the laboratory and no hybrid breakdown, the genetic trajectory was highly repeatable: replicates rapidly became dominated by alleles from the fitter parent. In a second cross, between two populations showing similar fitness and significant F2 hybrid breakdown, alleles from alternative populations dominated different replicates. Swarms exhibited a general temporal trend of decreasing cytonuclear mismatch. Some patterns of differential introgression across the genome were strikingly congruent amongst swarm replicates, both within and between cross types, and reflected patterns of segregation distortion previously observed within controlled crosses between the same parental populations. Differences in heterozygosity between the sexes, and evidence for a previously suspected sex-distortion locus, suggest that complex interactions between sex and genotype influence hybrid swarm outcome.