Step-by-step Solution:

\[ \textbf{Statements:} \] \[ 1.\; \text{Some men are great.} \quad 2.\; \text{Some men are wise.} \] \[ \textbf{Conclusions:} \] \[ 1.\; \text{Men are either great or wise.} \] This implies that all men must be in the set of either ``great'' or ``wise''. But the statements only guarantee that \emph{some} men are great and \emph{some} men are wise. Thus, this conclusion does \textbf{not} follow. \[ 2.\; \text{Some men are neither great nor wise.} \] The given statements provide no information about men outside the sets ``great'' and ``wise''. It is possible that all men are in one or both of these sets, or that some men are outside them. Hence, this conclusion also does \textbf{not} follow. \[ \boxed{\text{Correct Answer: Neither Conclusion 1 nor Conclusion 2 follows.}} \]