The aim of this study was to determine the relationship between fineness characteristics and resistance of Ch’aku llama fleeces. Seventy-six llamas from the breeding stock of the South American Camelids Research Center -CICAS- La Raya, Peru were sampled. Fibre fineness characteristics were determined (Average Fibre Diameter [MDF, µm], Variability Coefficient of Average Fibre Diameter [CVMDF,%], Comfort Factor [FC,%], Curvature, curl [CRV, °/mm], Spinning Fineness [SF, µm]) in an Optical Fibre Diameter Analyzer (OFDA 2000®) and fleece strength characteristics (Staple Length [LM, mm], Resistance to Traction [RT, N / ktex], and Position of Break [POB,%]) using the Staple Length and Strength Instrument (SL&SI). A randomized complete design with a factorial arrangement was used, using parametric and non-parametric tests. The results indicated effect of sex, age and sex*age, on the characters under study (p<0.05), where the best fineness is attributed to female llamas, 2-3 year old llamas and 2-3 year old female llamas; however, the highest LM and RT corresponds to male llamas (10.28 cm and 69.11 N/ktex, respectively), and the lowest in animals >5 years (57.61 N/ktex). The POB close to 50% is undesirable due to the thinning in a period of biennial fibre growth. Significant correlation was found between fineness characteristics and limited with resistance characteristics. The fibre of Ch’aku llamas in the CICAS-La Raya has important characteristics of fineness and resistance, but without linking between both types of characteristics.