  The nearby bright M-dwarf star L~98-59 has three terrestrial-sized planets.
One challenge remaining in characterizing atmospheres around such planets is
that it is not known a priori whether they possess any atmospheres. Here we
report the study of the atmospheres of L~98-59~c and L~98-59~d using the
near-infrared spectral data from the G141 grism of HST/WFC3. We can reject the
hypothesis of a clear atmosphere dominated by hydrogen and helium at a
confidence level of $\sim$ 3~sigma for both planets. Thus they may have a
primary hydrogen-dominated atmosphere with an opaque cloud layer, or have lost
their primary hydrogen-dominated atmosphere and re-established a secondary thin
atmosphere, or have no atmosphere at all. We cannot distinguish between these
scenarios for the two planets using the current HST data. Future observations
with JWST would be capable of confirming the existence of atmospheres around
L~98-59~c and d and determining their compositions.
