  We show analytic results for the irreducible charge and spin
susceptibilities, $\chi_0 (\omega, {\bf Q})$, where ${\bf Q}$ is the momentum
transfer between the nodes in d-wave superconductors. Using the BCS theory and
a circular Fermi surface, we find that the singular behavior of the irreducible
charge susceptibility leads to the dynamic incommensurate charge collective
modes. The peaks in the charge structure factor occur at a set of wave vectors
which form an ellipse around ${\bf Q}_{\pi}=(\pi,\pi)$ and ${\bf Q}_0=(0,0)$ in
momentum space with momentum dependent spectral weight. It is also found that,
due to the non-singular irreducible spin susceptibility, an extremely strong
interaction via random phase approximation is required to support the magnetic
peaks near ${\bf Q}_{\pi}$. Under certain conditions, the peaks in the magnetic
structure factor occur near ${\bf Q}=(\pi,\pi (1 \pm \delta))$ and $(\pi (1 \pm
\delta),\pi)$.
