The nonlocal dynamical response of a ballistic nanobridge to an applied potential oscillating with frequency ω is considered. It is shown that, in addition to the active conductance, there is also a reactive contribution. This contribution turns out to be inductive for relatively small frequencies ω. For bigger frequencies the current response is either inductive or capacitive, depending on the ratio of ωL/v(F), where L is the length of the bridge and v(F) is the Fermi velocity.