To examine: (1) relationships between brain structure, and concurrently assessed neurological and behavioural functioning, in infants born preterm at term-equivalent age (TEA; approximately 38-44wks); and (2) whether brain structure-function relationships differ between infants born very (24-29wks) and moderate-late (32-36wks) preterm. A total of 257 infants (91 very preterm, 166 moderate-late preterm; 120 males, 137 females) had structural magnetic resonance imaging (MRI) and neurological and behavioural assessments (Prechtl's general movements assessment, Neonatal Intensive Care Unit Network Neurobehavioral Scale [NNNS] and Hammersmith Neonatal Neurological Examination [HNNE]). Two hundred and sixty-three infants (90 very preterm, 173 moderate-late preterm; 131 males, 132 females) had diffusion MRI and assessments. Associations were investigated between assessment scores and global brain volumes using linear regressions, regional brain volumes using Voxel-Based Morphometry, and white matter microstructure using Tract-Based Spatial Statistics. Suboptimal scores on some assessments were associated with lower fractional anisotropy and/or higher axial, radial, and mean diffusivities in some tracts: NNNS attention and reflexes, and HNNE total score and tone, were associated with the corpus callosum and optic radiation; NNNS quality of movement with the corona radiata; HNNE abnormal signs with several major tracts. Brain structure-function associations generally did not differ between the very and moderate-late preterm groups. White matter microstructural alterations may be associated with suboptimal neurological and behavioural performance in some domains at TEA in infants born preterm. Brain structure-function relationships are similar for infants born very preterm and moderate-late preterm. Brain volume is not related to neurological/behavioural function in infants born preterm at term. White matter microstructure is related to some neurological/behavioural domains at term. Brain-behaviour relationships are generally similar for infants born very preterm and moderate-late preterm.