We investigated the comorbidity of low language and reading skills in 6- to 8-year-old monolingual Polish-speaking children (N = 962) using three different approaches: norming data to determine the prevalence of co-morbid difficulties, group comparisons of profiles on key cognitive-linguistic measures, and a case series analysis examining the frequency of single versus multiple deficits. We identified four groups of children based on their oral language and reading skills: children with low oral language skills alone, low reading skills alone, comorbid low language/reading skills, and typically developing chronological-age controls. We characterized the four groups (n = 38 per group) in terms of oral language and reading skills measured with normed test batteries, and in terms of the cognitive-linguistic profiles measured by the phonological awareness test (PA), rapid automatized naming test (RAN), and nonword repetition tests (NWR). We found that 24-31% of children with one type of difficulty had comorbid difficulties in the other domain. All groups differed significantly in cognitive-linguistic profiles. For each measure, the comorbid group had the lowest results. The group of children with isolated low language skills had better results than the comorbid group in (1) Sentence repetition (sub-test in an oral language test), (2) discrimination-based, blending-based, and elision-based PA sub-tests, (3) RAN (both digits and letters). The group with isolated low reading skills had better results than the comorbid group in: (1) discrimination-based PA sub-test, (2) NWR tests. The results indicate differences in cognitive-linguistic profiles between the groups with low language and/or low reading skills. They highlight the need to control for both types of difficulties in researching low language and/or reading skills, and to screen for comorbid issues while diagnosing children.