  We study the normal and the superconducting properties in noncentrosymmetric
heavy fermion superconductors CeRhSi$_3$ and CeIrSi$_3$. For the normal state,
we show that experimentally observed linear temperature dependence of the
resistivity is understood through the antiferromagnetic spin fluctuations near
the quantum critical point (QCP) in three dimensions. For the superconducting
state, we derive a general formula to calculate the upper critical field
$H_{c2}$, with which we can treat the Pauli and the orbital depairing effect on
an equal footing. The strong coupling effect for general electronic structures
is also taken into account. We show that the experimentally observed features
in $H_{c2}\parallel \hat{z}$, the huge value up to 30(T), the downward
curvatures, and the strong pressure dependence, are naturally understood as an
interplay of the Rashba spin-orbit interaction due to the lack of inversion
symmetry and the spin fluctuations near the QCP. The large anisotropy between
$H_{c2}\parallel \hat{z}$ and $H_{c2}\perp \hat{z}$ is explained in terms of
the spin-orbit interaction. Furthermore, a possible realization of the
Fulde-Ferrell- Larkin-Ovchinnikov state for $H\perp \hat{z}$ is studied. We
also examine effects of spin-flip scattering processes in the pairing
interaction and those of the applied magnetic field on the spin fluctuations.
We find that the above mentioned results are robust against these effects. The
consistency of our results strongly supports the scenario that the
superconductivity in CeRhSi$_3$ and CeIrSi$_3$ is mediated by the spin
fluctuations near the QCP.
