  We calculate pseudorapidity ($\eta$) asymmetry in $pA$ and $dA$ collisions in
a pQCD-improved parton model. With the calculations tuned to describe existing
spectra from $pp$ collisions and asymmetric systems at midrapidity and large
rapidities at FNAL and RHIC energies, we investigate the roles of nuclear
shadowing and multiple scattering on the observed asymmetry. Using this
framework, we make predictions for pseudorapidity asymmetries at high $p_T$ and
large $\eta$ in a wide range of energies up to LHC.
