In this study a total of 6499 records were obtained for fibre diameter (FD) and coefficient of variation of FD (CV), 3283 records for greasy fleece weight (GFW), staple length (SL) and shearing interval (SI) and 1802 records of textile value index (TV) obtained from an experimental herd of alpacas exploited in the Peruvian Altiplano. The estimated heritabilities were: 0.412 ± 0.015 (FD), 0.321 ± 0.013 (CV), 0.098 ± 0.016 (GFW), 0.070 ± 0.011 (SL), 0.061 ± 0.012 (SI) and 0.163 ± 0.017 (TV). No significant genetic correlation was found for the pairs FD-CV and CV-GFW whilst the pairs FD-GFW, FD-SI and FD-TV had significant genetic correlations of, respectively, 0.405 ± 0.081, - 0.395 ± 0.078 and - 0.746 ± 0.049. No significant correlations were found for SL except for the pair SL-SI (0.397 ± 0.099). The TV index also showed significant genetic correlations with CV of 0.125 ± 0.061 and with GFW of 0.490 ± 0.070. All estimates of permanent environmental effects (c2) associated with the six analysed traits were statistically significant ranging from 0.008 for SI to 0.259 for CV. Total repeatability for the analysed traits was low for SI (0.069) and SL (0.090), moderate for TV (0.299) and GFW (0.316) and high for FD (0.578) and CV (0.579). The permanent environmental effect associated with CV is significantly correlated with those of the other traits except for FD. The permanent environmental effects associated with GFW and SL seemed to be basically the same (estimated correlation of 0.916 ± 0.062). The permanent environmental effect for TV is highly correlated with those associated with GFW (0.498 ± 0.058) and SL (0.750 ± 0.137). Expected selection response for TV was higher when FD was considered as selection goal instead of TV itself. It would, therefore, be more efficient to use FD rather than empirical indices as selection criterion to increase textile value in Peruvian alpacas. The reported genetic parameters and correlation matrices can be useful to implement multitrait breeding value estimations for alpaca selection. © 2008 Elsevier B.V. All rights reserved.