  We study nonperiodic tilings of the line obtained by a projection method with
an interval projection structure. We obtain a geometric characterisation of all
interval projection tilings that admit substitution rules and describe the set
of substitution rules for each such a tiling. We show that each substitution
tiling admits a countably infinite number of nonequivalent substitution rules.
We also provide a complete description of all tilings of the line and half line
with an interval projection structure that are fixed by a substitution rule.
Finally, we discuss how our results relate to renormalization properties of
interval exchange transformations (with two or three intervals).
