  We present a bounded modified realisability and a bounded functional
interpretation of intuitionistic nonstandard arithmetic with nonstandard
principles.
  The functional interpretation is the intuitionistic counterpart of Ferreira
and Gaspar's functional interpretation and has similarities with Van den Berg,
Briseid and Safarik's functional interpretation but replacing finiteness by
majorisability.
  We give a threefold contribution: constructive content and proof-theoretical
properties of nonstandard arithmetic; filling a gap in the literature; being in
line with nonstandard methods to analyse compactness arguments.
