  We use characteristic functions to construct alpha(x)-multistable measures
and integrals, where the measures behave locally like alpha-stable measures,
but with the stability index alpha(x) varying with time x. This enables us to
construct alpha(x)-multistable processes on R, that is processes whose scaling
limit at time x is an alpha(x)-stable process. We present several examples of
such multistable processes and examine their localisability.
