The average age of 8 men is increased by 2 years when two of them whose ages are 21 years and 23 years are replaced by two new men. Find the average age of the two new men.

Suppose that the average age of of 8 men was $x$

Given that average age of 8 men is increased by 2 years when two of them whose ages are 21 years and 23 years are replaced by two new men

$\begin{array}{rcl}\frac{8x-21-23+a+b}{8}& =& x+2\\ 8x-44+a+b& =& 8x+16\\ a+b& =& 60\end{array}$

Therefore, the average age of other two men is $\frac{60}{2}=\boxed{30}$