Objective: Interest continues in neuropsychological measures as cross-disorder intermediate phenotypes in understanding psychopathology. A central question concerns their specificity versus generalizability to particular forms of psychopathology, particularly for executive functioning (EF) and response speed. Three conceptual models examining these relationships were tested to clarify this picture at different levels in the diagnostic hierarchy. Method: Participants (total n = 641, age 18-60) yielded complete structured diagnostic interviews and a neuropsychological test battery comprising measures of executive function, processing speed, and IQ. Repeated measures multivariate analysis of variance, linear regression, and structural equation modeling (SEM) were used to test (a) a specificity model, which proposes that individual disorders are associated with component EF processes and speed; (b) a severity model, which proposes that the total number of comorbid disorders explain poor EF and/or slow speed; and (c) a higher-order dimensional model, which proposes that internalizing versus externalizing disorders are differentially related to EF or speed. Results: EF effects were best explained by a specificity model, with distinct aspects of EF related to attention deficit hyperactivity disorder versus antisocial substance use disorders. Speed, on the other hand, emerged as a general indicator of externalizing psychopathology in the dimensional model, as well as overall severity of psychopathology in the severity model. Conclusions: Granular approaches are likely to be most productive for linking EF to psychopathology, whereas response speed has underused potential as an endophenotype for psychopathology liability. Results are discussed in terms of an integrated conceptualization of neuropsychological processes and putative neural systems involved in general and specific aspects of psychopathology.