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In this paper we introduce an extended interval arithmetic structure. 4'* involving infinite intervals which is a further extension of the extended interval arithmetic. 4/using finite intervals and an extended set of basic interval arithmetic operations. The structure. 4* is compared to other known interval arithmetic structures. We discuss three possible directions of extensions of the conventional real interval arithmetic S", which have been developed as algebraic structures during the last two decades and which have proved to be useful for applications in interval analysis: i) the extension. 4/by supplementary nonstandard interval-arithmetic operations, ii) the extensions I (R*) and. 4/* by infinite intervals and iii) the extension Jf by generalized intervals. These three types of extended structures have been introduced in a logically consecutive order by using uniform notations and can be considered as substructures of a single …