  In this work, two-cluster modes are studied in a system of globally coupled
Kuramoto-Sakaguchi phase oscillators with inertia. It is shown that these
regimes can be of two types: with a constant intercluster phase difference
rotating at the same frequency (according to the analysis, such regimes are
always unstable) and with a periodically changing (taking into account the
multiplicity of $2\pi$) phase mismatch. The issues of existence and stability,
emergence and destruction of two-cluster modes are studied depending on the
parameters: effective mass (responsible for inertial processes in the model
system under consideration) and phase shift in the coupling function. The
analytical results are confirmed and supplemented by numerical simulation of
the rotators (second order) interacting globally through the mean field.
