  The ANNRI-Gd collaboration studied in detail the single $\gamma$-ray spectrum
produced from the thermal neutron capture on $^{155}$Gd and $^{157}$Gd in our
previous publications. Gadolinium targets were exposed to a neutron beam
provided by the Japan Spallation Neutron Source (JSNS) in J-PARC, Japan. In the
present analysis, one new additional coaxial germanium crystal was used in the
analysis in combination with the fourteen germanium crystals in the cluster
detectors to study the angular correlation of the two $\gamma$ rays emitted in
the same neutron capture. We present for the first time angular correlation
functions for two $\gamma$ rays produced during the electromagnetic cascade
transitions in the (n, $\gamma$) reactions on $^{\rm 155}$Gd and $^{\rm
157}$Gd. As expected, we observe the mild angular correlations for the strong,
but rare transitions from the resonance state to the two energy levels of known
spin-parities. Contrariwise, we observe negligibly small angular correlations
for arbitrary pairs of two $\gamma$ rays produced in the majority of cascade
transitions from the resonance state to the dense continuum states.
