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We study the microlocal analyticity of solutions $u$ of the nonlinear equation $$u_t=f(x,t,u,u_x)$$ where $f(x,t,{\zeta }_0,\zeta )$ is complex-valued, real analytic in all its arguments and holomorphic in $({\zeta }_0,\zeta )$. We show that if the function $u$ is a $C^2$ solution, $\sigma \in \text{Char}{L}^u$ and $\frac{1}{i}\sigma \left([L^u,\overline{L^u}]\right)\<0$ or if $u$ is a $C^3$ solution, $\sigma \in \text{Char}{L}^u$, $\sigma \left([L^u,\overline{L^u}]\right)=0$, and $\sigma \left([L^u,[L^u,\overline{L^u}]]\right)\ne 0$, then $\sigma \notin W{F}_{a}u$. Here $W{F}_{a}u$ denotes the analytic wave-front set of $u$ and Char$L^u$ is the characteristic set of the linearized operator. When $m=1$, we prove a more general result involving the repeated brackets of $L^u$ and $\overline{L^u}$ of any order.