  In this paper we analyze a coupling between the very large jumps in physical
and operational times as applied to anomalous diffusion. The approach is based
on subordination of a skewed Levy-stable process by its inverse to get two
types of operational time - the spent and the residual waiting time,
respectively. The studied processes have different properties which display
both subdiffusive and superdiffusive features of anomalous diffusion underlying
the two-power-law relaxation patterns.
