11. Let the sequence $a_{1}, a_{2}, \cdots, a_{n}, \cdots$ satisfy $a_{1}=a_{2}=1, a_{3}=2$, and for any positive integer $n$, $a_{n} \cdot a_{n+1} \cdot a_{n+2} \neq 1$. Also, $a_{n} \cdot a_{n+1} \cdot a_{n+2} \cdot a_{n+3}=a_{n}+a_{n+1}+a_{n+2}+$ $a_{n+3}, a_{1}+a_{2}+\cdots+a_{100}$ has the value $\qquad$ .
11. 200.

From the conditions, we derive $a_{4}=4, a_{5}=1, a_{6}=1, a_{7}=2, a_{8}=4$, so the sequence $\left\{a_{n}\right\}$ is a periodic sequence with a period of 4, $a_{n+4}=a_{n}$. Therefore, $a_{1}+a_{2}+\cdots+a_{100}=25\left[a_{1}+a_{2}+a_{3}+a_{4}\right]=200$.