  The linear response is studied in globally coupled oscillator systems
including the Kuramoto model. We develop a linear response theory which can be
applied to systems whose coupling functions are generic. Based on the theory,
we examine the role of asymmetry introduced to the natural frequency
distribution, the coupling function, or the coupling constants. A remarkable
difference appears in coexistence of the divergence of susceptibility at the
critical point and a nonzero phase gap between the order parameter and the
applied external force. The coexistence is not allowed by the asymmetry in the
natural frequency distribution but can be realized by the other two types of
asymmetry. This theoretical prediction and the coupling-constant dependence of
the susceptibility are numerically verified by performing simulations in
$N$-body systems and in reduced systems obtained with the aid of the
Ott-Antonsen ansatz.
