  We report the results of the first joint observation of the KAGRA detector
with GEO600. KAGRA is a cryogenic and underground gravitational-wave detector
consisting of a laser interferometer with three-kilometer arms, and located in
Kamioka, Gifu, Japan. GEO600 is a British--German laser interferometer with 600
m arms, and located near Hannover, Germany. GEO600 and KAGRA performed a joint
observing run from April 7 to 20, 2020. We present the results of the joint
analysis of the GEO--KAGRA data for transient gravitational-wave signals,
including the coalescence of neutron-star binaries and generic unmodeled
transients. We also perform dedicated searches for binary coalescence signals
and generic transients associated with gamma-ray burst events observed during
the joint run. No gravitational-wave events were identified. We evaluate the
minimum detectable amplitude for various types of transient signals and the
spacetime volume for which the network is sensitive to binary neutron-star
coalescences. We also place lower limits on the distances to the gamma-ray
bursts analysed based on the non-detection of an associated gravitational-wave
signal for several signal models, including binary coalescences. These analyses
demonstrate the feasibility and utility of KAGRA as a member of the global
gravitational-wave detector network.
