This paper aims at highlighting the overlapping between the qualification mismatch and the skill mismatch, using a specific Italian data set drawn from PIAAC survey (2012). The main concern, regarding skills and competences, is that they may be gathered and accumulated, but also potentially become obsolete, thus, qualifications (formally recognized) do not necessarily correspond to used skills and competences. Measuring skill mismatch is evidently problematic as there are not many direct information regarding skills at the workplace. Usually information comes from self-reported measures (correspondence of tasks performed at work) or comparing indicators of proficiency and use at work, methodologies prone to bias. Skill mismatch arises from several structural modifications in countries economy and social demographic events such as migration. And skill mismatch and qualification mismatch are a common phenomenon among foreign workers. The levels of both their qualifications and the skills used at work are rarely well-match among this particular target group. Besides, the Italian system not always is able to adequately assess, recognize and validate qualifications and/or skills and competences possessed by immigrants who are applying for working positions. PIAAC makes it possible to compare qualifications, information processing skills (literacy and numeracy) and skills required on the job, for specific target groups. The Survey of Adult Skills provides a measure of skill mismatch: it arises when workers have higher or lower skills proficiency (measured) than that required by their jobs (self-reported information). The relationship between skill mismatch and labour market outcomes involves different approaches and implications at policy level in inclusive societies, especially considering economic and socio-demographic factors. Among the three proficiency cognitive domains of PIAAC, we focused on literacy mismatch as (compared to numeracy) is a parameter of high relevance for the chosen target group (migrants). In fact it indicates the adaptability in the host working context due to language difficulties. Findings in PIAAC show that foreign workers are three times more likely than natives to be under-skilled in literacy. And the difference arises if we consider the time parameter ("since how long they have been living in Italy"): less than 5 years residents are even more under-skilled (more than 30%). Besides, foreign workers are overqualified (26.5%) much more than Italians (12.4%) and also two times more likely to be over-qualified than natives. But it is worth noting that among overqualified workers (with a higher qualification than the one needed to carry out the specific job), foreign workers seem to lack the necessary skills. This discrepancy is an important element to understand social integration dynamics and thus orientate policies.