  A classical computation of vector bremsstrahlung in ultrarelativistic
gravitational-force collisions of massive point particles is presented in an
arbitrary number d of extra dimensions. Our method adapts the post-linear
formalism of General Relativity to the multidimensional case. The total emitted
energy, as well as its angular and frequency distribution and characteristic
values, are discussed in detail.
  For an electromagnetic mediation propagated in the bulk, the emitted energy
$E_{em}$ of scattering with impact parameter b has magnitude $E_{em} \sim e^4
e'^2 \gamma^{d+2}/(m^2 b^{3d+3})$, with dominant frequency $\omega_{em} \sim
\gamma^2/b$. For the gravitational force the charge emits via vector field,
propagated in the bulk, energy $E_{rad}\sim[G_D m' e]^2 \gamma^{d+2}/b^{3d+3}$
for $d \geq 2$, with dominant frequency $\omega\sim\gamma^2/b$ and energy
$E_{rad}\sim[G_5 m' e]^2\gamma^{3}\ln \gamma/b^{6}$ for $d=1$, with most of the
energy coming from a wide frequency region $\omega \in [\gamma/b),\gamma^2/b]
$. For the UED model with extra space volume $V=(2\pi R)^d$ the emitted energy
is $E_{UED}\sim (b^{d}/V)^2 E_{rad}$. Finally, for the ADD model, including
four dimensions, the electromagnetic field living on 3-brane, loses on emission
the energy $E_{ADD}\sim[G_D m'e]^2\gamma^{3}/(V b^{2d+3})$, with characteristic
frequency $\omega_{ADD}\sim\gamma/b$.
  The contribution of the low frequency part of the radiation (soft photons) to
the total radiated energy is shown to be negligible for all values of d. The
domain of validity of the classical result is discussed. The result is analyzed
from the viewpoint of the deWitt - Brehme - Hobbs equation (and corresponding
equations in higher dimensions).
