Recent advances in the understanding of the relations between cognitive abilities and academic skills have helped shape a better understanding of which cognitive processes may underlie different types of SLD (Flanagan, Fiorello, & Ortiz, 2010). Similarities and differences in cognitive-achievement relations for children with and without SLDs have not been extensively studied. This study examined whether cognitive-achievement relations are similar among groups of children with SLD in reading (n = 181), math ( n = 231), and writing (n = 149), when compared to children without SLD (n = 300) using the Woodcock-Johnson-Third Edition (WJ-III; Woodcock, McGrew, & Mather, 2007). Multi-group structural equation modeling (SEM) was used to examine cognitive-achievement relations. A three-stratum model of cognitive abilities based on Cattell-Horn-Carroll (CHC) theory was used in the analysis. Results showed that the factor structure and factor loadings of the CHC model were invariant among groups, and SLD group membership moderated the magnitude of several cognitive-achievement relations: (a) Knowledge (K0), Short-term Memory (Gsm), and Quantitative Reasoning (RQ) were important predictors of Basic Reading Skills (BRS) across all groups, but Perceptual Speed (PS) was also an important predictor of BRS for individuals with SLD in reading; (b) K0 and RQ were important predictors of Reading Comprehension (RC) for all groups, but RQ had a stronger relation to RC for individuals with SLD in reading; (c) PS, and Gsm were important predictors for Math Calculation Skills (MCS) in all groups, and RQ predicted MCS for all groups except those with SLD in math; (d) RQ and K0 predicted Applied Math (AM) for all groups, but visualization (VZ) was also an important predictor of AM for individuals with SLD in math and SLD in writing; and (e) Gc, RQ, VZ, Memory Span (MS), and Rapid Naming (RN) were important predictors of written expression, and the only difference between groups was those with SLD in math relied slightly more on Gc. Results suggest that individuals with SLD in specific academic areas may rely on some different cognitive abilities as a way to compensate for deficits in academic skills. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]