  We establish Cram\'er type moderate deviation (MD}) results for heavy trimmed
L-statistics; we obtain our results under a very mild smoothness condition on
the inversion $F^{-1}$ ($F$ is the underlying distribution of i.i.d.
observations) near two points, where trimming occurs, we assume also some
smoothness of weights of the L-statistic. Our results complement previous work
on Cram\'er type large deviations (LD) for trimmed L-statistics by Gribkova
(2016) and Callaert et al. (1982).
