In this paper, it is established, in the case of graphs, that time-like extremal surfaces of dimension $1+n$ in the Minkowski space of dimension $1+n+m$ can be described by a symmetric hyperbolic system of PDEs with the very simple structure (reminiscent of the inviscid Burgers equation) $$ \partial_t W + \sum_{j=1}^n A_j(W)\partial_{x_j} W =0,\;\;\;W:\;(t,x)\in\mathbb{R}^{1+n} \rightarrow W(t,x)\in\mathbb{R}^{n+m+\binom{m+n}{n}}, $$ where each $A_j(W)$ is just a $\big(n+m+\binom{m+n}{n}\big)\times\big(n+m+\binom{m+n}{n}\big)$ symmetric matrix depending linearly on $W$.