Gene insertion and deletion are considered as the basic operations in DNA processing and RNA editing. Based on these evolutionary transformations, a computing model has been formulated in formal language theory known as insertion-deletion systems. Recently, in [6], a new computing model named Matrix insertion-deletion system has been introduced to model various bio-molecular structures such as hairpin, stem and loop, pseudoknot, attenuator, cloverleaf, dumbbell that occur at intramolecular level. In this paper, we model some of the intermolecular structures such as double strand languages, nick languages, hybrid molecules (with R-loops), holliday structure, replication fork and linear hybridization (ligated) languages using Matrix insertion-deletion system. In [2], the ambiguity in gene sequence was defined as deriving more than one structure for a single gene sequence. Here, we propose a different view of understanding the ambiguity in gene sequences: A gene sequence is obtained by more than one way such that their intermediate sequences are different. We further classify the ambiguity into many levels based on the components axiom, string (order of deletion/insertion) and contexts (order of the used contexts). We notice that some of the inter and intramolecular structures obey the newly defined ambiguity levels. © 2011 The authors and IOS Press. All rights reserved.