Understanding of preterm infant cognitive competences across the first year of life is limited regarding the developmental constructs of continuity, stability, coherence, and predictive validity as well as how they manifest by age and country of origin. This prospective longitudinal study examined and compared mean-level continuity, individual-differences stability, and associations among several cognitive competences as well as their predictive validity across the first year of life in preterm infants (gestational age range = 26-33 weeks) from Chile (n = 47), the United Kingdom (n = 48), and the United States (n = 50). Multiple cognitive competences (visual acuity measured with the Teller acuity card procedure; information processing duration of visual fixation and novelty preference examined with the Fagan Test of Infant Intelligence; Bayley Mental and Psychomotor Indexes) were evaluated at five different ages in preterm infants between 2 and 12 months in each country. The effects of infant age, country, and their interaction were examined. Visual acuity increased over time with different trajectories across countries, whereas duration of visual fixation decreased; both were stable across time. Novelty preference demonstrated continuity, but not stability across time and country. Associations among different cognitive competences varied by country. Across countries, duration of visual fixation predicted the Bayley Mental Development Index, and visual acuity predicted the Bayley Psychomotor Development Index. Cognitive competences develop in similar and dissimilar ways across the first year of life in infants born preterm from different countries. Cultural specificities and age variations are discussed. Study findings underscore the necessity to attend to specificities of domain, age, and place when assessing preterm infants' cognitive competences.