  We investigate the Higgs sector of a nonlinear supersymmetric standard model
at LEP 1 and LEP 2, as well as at future linear $e^+ e^-$ colliders with $\sqrt
s = 500$, 1000, and 2000 GeV. The LEP 1 data do not put any constraints on the
parameters of the model, and allow a massless Higgs boson in particular. For
LEP 2, there are remarkable differences between the Higgs productions at $\sqrt
s = 175$ GeV on the one hand and that at $\sqrt s = 192$ GeV and 205 GeV on the
other hand. The case for $\sqrt s = 175$ GeV is similar to LEP 2, whereas those
for $\sqrt s = 192$ GeV and 205 GeV will be able to give experimental
constraints on the parameters. Finally the $e^+ e^-$ colliders with $\sqrt s =
500$, 1000, and 2000 GeV are most probably able to test the model conclusively.
