In communication, people often intend to convey more than the words they literally utter. The literal, semantic meaning of a sentence can be enriched by its implicit, pragmatic meaning. The term implicature refers to an interpretation of what a speaker didnt explicitly say but intended to say. Two broad categories of implicatures can be distinguished. On the one hand, there are conversational implicatures of which the scalar implicature is the most widely investigated subtype. On the other hand, there are conventional implicatures which have rarely been experimentally investigated. This dissertation discusses both types of implicature from a developmental point of view. In scalar implicature research, it has often been concluded that adults are more pragmatically competent than children. This was interpreted as indirect evidence that inferring a scalar implicature is cognitively effortful and requires working memory. Other evidence showing that working memory is involved in scalar implicature processing was presented among others by Bott and Noveck (2004) and De Neys and Schaeken (2007). However, Katsos and Bishop (2011) showed that certain task characteristics can conceal childrens pragmatic competence and therefore lead to the wrongly drawn conclusion that children are pragmatically incompetent. This shows that it is worth investigating the role of age, task characteristics and working memory in implicature research, especially for conventional implicatures of which little experimental information is available. In Chapter 2 of this dissertation, a scalar implicature study is described in which we look at the effect of age, working memory capacity and task features on processing the scalar implicature from some. Age and task characteristics were found to greatly influence the number of pragmatic responses whereas an effect of working memory was absent.In Chapters 3 to 7, the conventional implicature stemming from but combined with so and nevertheless- was investigated. Our primary interest was finding out whether the conventional meaning of these instruction words is indeed understood. Secondly, we investigated the effect of age, working memory and task characteristics as well. Our results showed that adults seem to have a pretty good understanding of the conventional meaning of these words whereas childrens performance revealed lower competence. In fact, using a three-point scale instead of a binary response format in Chapter 5 seemed to reveal that these sentences are really difficult for children and that they often dont know what they have to answer. With regards to the working memory effect, we found no influence of working memory on conventional implicature processing. This leads to the conclusion that conventional implicature processing happens automatically.