Methods for providing nutrition and for enhancing neurological development of preterm infants are disclosed. Also disclosed is an improved nutritional composition containing specified amounts of DHA and AA as well as their precursor essential fatty acids alpha-linolenic and linoleic acids. The methods involve feeding LCP supplemented, nutrient-enriched formulas for an extended feeding regimen, typically until at least 3 months corrected age (CA), preferably to 6 or even 12 months CA. The neurological developments, for example, visual development, motor development and language development were enhanced without findings of anthropometric growth faltering or inhibition.