  We evaluate the dynamic structure factor $S(q,\omega)$ of interacting
one-dimensional spinless fermions with a nonlinear dispersion relation. The
combined effect of the nonlinear dispersion and of the interactions leads to
new universal features of $S(q,\omega)$. The sharp peak $S\propto
q\delta(\omega-uq)$, characteristic for the Tomonaga-Luttinger model, broadens
up; $S(q,\omega)$ for a fixed $q$ becomes finite at arbitrarily large $\omega$.
The main spectral weight, however, is confined to a narrow frequency interval
of the width $\delta\omega\sim q^2/m$. At the boundaries of this interval the
structure factor exhibits power-law singularities with exponents depending on
the interaction strength and on the wave number $q$.
