In hybrid zones populations that are otherwise allopatric meet and produce hybrids. One of the most well-known hybrid zones occurs throughout much of Europe between the hooded and carrion crows. Even though these species (or subspecies) of crows look very different, genetic differentiation is weak, and introgression seems to be common. In a spatial simulation that was based on empirically estimated values, we investigated how introgressing alleles that would confer some fitness advantage would flow across the zone. The advantage was assumed to be some unknown factor that enhanced survival for carriers relative to non-carriers. We varied the yearly survival advantage between 0 to 10% and recorded how this would affect zone shape and position. In the simulation we cycled ‘yearly’ events such as reproduction, mortality and juvenile dispersal. We started the simulation by equipping all individuals of one crow type outside the zone with a homozygotic set of the beneficial allele. At all levels of advantage the allele first rapidly became fixed in the donator crow type, then transgressed into the receiving type more slowly and finally became fixed in all individuals. The time until fixation varied from around 176 yr for a 10% advantage to around 20 000 yr for 0% advantage. An exciting discovery was that the position of the zone would move during the introgression but then stop. The reason is that the beneficial allele would be common in the donating type but not in the receiving type during the introgression event. At large the crow hybrid zone appears to have been stable for a long time but there have been small recent northward movements of carrion crows in both Scotland and Denmark. We suggest that introgression by itself is a factor that should be considered as an explanation for why hybrid zones move temporarily.