The authors consider the initial-boundary value problem for a nonlinear hyperbolic equation of second order in flux formulation, \[ \text{grad }p+ \underline b(\underline u)= \underline O\quad\text{in }\Omega\times (0,T], \] \[ p_{tt}+ \text{div }\underline u= f\quad\text{in }\Omega\times (0,T], \] where \(p\), \(f\) are scalars and \(\underline u\), \(\underline b(\cdot)\) are vector-valued. \(\underline b(\cdot)\) describes the nonlinearity. For the discretization in space, a mixed finite element method is used. Firstly, the existence and uniqueness of the spatially discrete solution is proved. Then, the authors prove optimal a priori error estimates for \(p\), \(p_t\) and \(\underline u\) in the \(L^\infty(0,T; L^2(\Omega))\)-norm.