In DNA processing and RNA editing, gene insertion and deletion are considered as the basic operations. Based on the above evolutionary transformations, a computing model has been formulated in formal language theory known as insertion-deletion systems. In this paper we study about ambiguity and complexity measures of these systems. First, we define the various levels of ambiguity (i = 0,1,2,3,4,5) for insertion-deletion systems. Next, we show that there are inherently i-ambiguous insertion-deletion languages which are j-unambiguous for the combinations (i, j) ∈ {(5,4), (4,2), (3,1), (3,2), (2,1),(0,1)}. Further, We prove an important result that the ambiguity problem of insertion-deletion system is undecidable. Finally, we define three new complexity measures TLength - Con, TLength - Ins, TLength - Del for insertion-deletion systems and analyze the trade-off between the newly defined ambiguity levels and complexity measures. © 2012 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering.