Alpaca is the most important fibre producer of South American camelid species, and an important income for the Andean communities. Nowadays, the fibre diameter is considered the main selection criterion in alpaca populations all over the world. However, fibre diameter increases with the age of the animals, and it would be preferable to select those animals that maintain a thm fibre throughout their life. The aim of this study is to describe the genetic relationship between fibre diameter at birth and its evolution over a lifetime. The analysis of the evolution of fibre diameter was studied as a longitudnal trait using the Bayesian procedure for the analysis of production functions. The results suggested that there is substantial genetic variation in fibre dameter at birth and also on the linear growth of fibre diameter. This confirms the need for a genetic programme to modify the evolution of the fibre dameter over time. However, selection to increase the growth of the fibre without a substantial reduction in the fibre diameter at birth seems implausible.