  We examine the evidence for multiband superconductivity and non s-wave
pairing in the non-centrosymmetric superconductor Nb$_{0.18}$Re$_{0.82}$, using
electrical transport, magnetization and specific heat measurements. In the
normal state, both the evolution of resistivity with temperature and with
magnetic field support a multiband picture. In the superconducting state, the
Werthamer, Helfand and Hohenberg (WHH) model cannot adequately describe the
temperature dependence of the upper critical field, $H_{c2}(T)$, over the whole
temperature range measured. In addition, the observed $H_{c2}(0)$ exceeds the
Pauli limit, suggesting non-s-wave pairing. Interestingly, the Kadowaki-Woods
ratio and Uemura plot reveal a behavior in Nb$_{0.18}$Re$_{0.82}$ which is
similar to that found in unconventional superconductors. The temperature
dependence of the lower critical field, $H_{c1}(T)$, follows an anomalous $T^3$
behavior and the derived normalized superfluid density ($\rho_s$) is well
explained using a nodeless two-gap description. Phase-fluctuation analysis
conducted on the reversible magnetization data, reveals a significant deviation
from the mean-field conventional s-wave behavior. This trend is interpreted in
terms of a non s-wave spin-triplet component in the pairing symmetry as might
be anticipated in a non-centrosymmetric superconductor where anti-symmetric
spin-orbit coupling plays a dominant role.
