Cognitive impairment in amyotrophic lateral sclerosis (ALS) is characterized by deficits on tests of executive functions however the contribution of processing speed is unknown. By contrast, multiple sclerosis (MS) is a disorder in which slowed processing speed is regarded as the core deficit, however, methodology is often confounded by tasks which depend on motor speed. MRI studies have revealed multi-system cerebral involvement in ALS, with evidence of reduced white matter volume and integrity in predominantly frontotemporal regions. The current study had two aims. Firstly, to investigate whether cognitive impairments in ALS and MS are due to executive dysfunction or slowed processing speed, independent of motor dysfunction. Secondly, to investigate the relationship between specific cognitive impairments and the integrity of distinct white matter tracts in ALS. Twenty-nine ALS patients, twenty-five MS patients, and matched healthy control groups were administered a dual task paradigm and processing speed tasks in which stimulus presentation times were manipulated. In addition background measures of executive functioning, working memory, verbal memory, and language were administered. White matter integrity was investigated using region-of-interest (ROI) and tract based spatial statistics (TBSS) analyses of diffusion MRI data. ALS patients did not show impairments in tests of processing speed, but deficits were revealed in the dual task, as well as background tests of executive functioning, working memory, and verbal memory. MS patients also exhibited deficits in the dual task as well as background tests of executive functioning, working memory, and verbal memory. However, in contrast to ALS patients, a processing speed deficit was also observed in MS. ROI analyses revealed significant differences in fractional anisotropy (FA) and mean diffusivity () between ALS patients and healthy controls. Reduced integrity was observed in the corticospinal tracts and prefrontal and temporal white matter tracts including uncinate fasciculus, inferior longitudinal fasciculus, and regions of the cingulum. Significant differences also emerged in the white matter underlying the superior, medial and inferior frontal gyri, and the temporal gyri. Similar group differences were found in the TBSS analyses; ALS patients displayed prominent changes in the corticospinal tract and corpus callosum as well as extensive changes in prefrontal and temporal tracts and association fibres. Correlations between task performance and ROI parameters revealed that dual task performance was associated with FA in the middle frontal gyrus white matter while letter fluency indices correlated with FA in the corpus callosum and corticospinal tracts. Furthermore, verbal memory performance correlated with FA in the inferior longitudinal fasciculus and working memory performance correlated with in uncinate fasciculus and hippocampal portion of the cingulum. Correlations with TBSS revealed significant associations between letter fluency indices and FA in the corticospinal tracts and anterior corpus callosum. The current study demonstrates that cognitive impairment in ALS is not due to slowed processing speed. Moreover dual task deficits are related to distinct prefrontal tract involvement in ALS, whilst fluency deficits may reflect decreasing callosal integrity. Deficits in working memory and verbal memory are related to white matter changes in fibre bundles connecting prefrontal, temporal, and limbic structures.