  The R\'enyi entanglement entropy (REE) of the states excited by local
operators in two-dimensional irrational conformal field theories (CFTs),
especially in Liouville field theory (LFT) and $\mathcal{N}=1$ super-Liouville
field theory (SLFT), has been investigated. In particular, the excited states
obtained by acting on the vacuum with primary operators were considered. {We
start from evaluating the second REE in a compact $c=1$ free boson field theory
at generic radius, which is an irrational CFT. Then we focus on the two special
irrational CFTs, e.g., LFT and SLFT. In these theories, the second REE of such
local excited states becomes divergent in early and late time limits. For
simplicity, we study the memory effect of REE for the two classes of the local
excited states in LFT and SLFT. In order to restore the quasiparticles picture,
we define the difference of REE between target and reference states, which
belong to the same class. The variation of the difference of REE between early
and late time limits always coincides with the log of the ratio of the fusion
matrix elements between target and reference states. Furthermore, the locally
excited states by acting generic descendent operators on the vacuum have been
also investigated. The variation of the difference of REE is the summation of
the log of the ratio of the fusion matrix elements between the target and
reference states, and an additional normalization factor. Since the identity
operator (or vacuum state) does not live in the Hilbert space of LFT and SLFT
and no discrete terms contribute to REE in the intermediate channel, the
variation of the difference of REE between target and reference states is no
longer the log of the quantum dimension which is shown in the 1+1-dimensional
rational CFTs (RCFTs).
