Carbon nanotube-infused fiber materials containing substantially parallel-aligned, infused carbon nanotubes are described herein. The carbon nanotube-infused fiber materials contain a fiber material and a layer of carbon nanotubes infused to the fiber material, where the infused carbon nanotubes are aligned substantially parallel to the longitudinal axis of the fiber material and at least a portion of the substantially parallel-aligned, infused carbon nanotubes are crosslinked to each other, to the fiber material, or both. Crosslinking can occur through covalent bonding or pi-stacking interactions, for example. The carbon nanotube-infused fiber materials can further contain additional carbon nanotubes that are grown on the layer of substantially parallel-aligned, infused carbon nanotubes. Composite materials containing the carbon nanotube-infused fiber materials and methods for production of the carbon nanotube-infused fiber materials are also described herein.