The aim of this study was to estimate the genetic parameters (heritability and genetic correlations) for characters associated with the uniformity of fibre diameter in fleece of young (tuis) alpacas of the Mallkini farm (Puno, Peru). Samples were taken from the thigh, mid-rib and shoulder of 1127 animals at the first shearing (573 males and 554 females) born in 2015 and 2016. The samples were analysed under the IWTO-12 standard of the Sirolan Laserscan equipment. The pedigree file had 10 481 alpacas giving a coefficient of inbreeding of 0.16%. The genetic parameters were estimated using ASReml and Pedigree Viewer software. The characters evaluated were the fibre diameter and its standard deviation, coefficient of variation and comfort factor. The genetic analysis was carried out using a multivariate animal model, which includes the additive genetic effect of the animal as a random effect; year of shearing, group/category and sex as fixed effects, and age of shearing as a linear covariable. The heritability for all the characteristics by body area was moderate (0.12 to 0.38) and for the mean of the three body areas was also moderate, except for the coefficient of variation (0.17 to 0.43). The genetic correlation between the fibre diameter and the standard deviation showed a high and positive value (0.80), while for the comfort factor it had a high and negative correlation (-0.93) and for the coefficient of variation was negative and low (-0.06). In conclusion, there is a high degree of genetic correlation between the fibre diameter and its standard deviation, so that selecting for both characters would reduce the variability of fineness in the fleeces.