In many expert and everyday reasoning contexts it is very useful to reason on the basis of defeasible assumptions. For instance, if the information at hand is incomplete we often use plausible assumptions, or if the information is conflicting we interpret it as consistent as possible. In this paper sequent-based argumentation, a form of logical argumentation in which arguments are represented by a sequent, is extended to incorporate assumptions. The resulting assumptive framework is general, in that some other approaches to reasoning with assumptions can adequately be represented in it. To exemplify this, we show that assumption-based argumentation can be expressed in assumptive sequent-based argumentation.