************************************************************************* 62085 We have searched all ASCA spectra of LMC SNRs for evidence of a nonthermal tail. Such a tail could arise from electrons accelerated within the shock to highly relativistic energy, and thus indicate cosmic ray creation. All SNRs with diameters <13 pc have hard components. Most of the observations are brief (~20ks), so characterizing the spectral form or placing a strong limit on a nonthermal contribution is difficult. A search for nonthermal emission is further complicated by the presence in some SNR's of an Fe K line, indicating a hard thermal component. We propose deep observations of 4 bright LMC SNRs, 0509-67.5, 0519-69.0, N23 and N63A, which will allow us to meaningfully compare the nonthermal luminosity with that of Galactic remnants (even in the presence of a hot thermal component). *************************************************************************