Biprojectivity and Biflatness for Convolution Algebras of Nuclear Operators For a locally compact group $G$, the convolution product on the space $\nN(L^p(G))$ of nuclear operators was defined by Neufang \cite{Neuf_PhD}. We study homological properties of the convolution algebra $\nN(L^p(G))$ and relate them to some properties of the group $G$, such as compactness, finiteness, discreteness, and amenability. Categories:46M10, 46H25, 43A20, 16E65