We provide a criterion for instability of equilibria of equations in the form $\dot x(t) = g(x_t', x_t)$, which includes neutral delay equations with state-dependent delay. The criterion is based on a lower bound $\Delta >0$ for the delay in the neutral terms, on regularity assumptions of the functions in the equation, and on spectral assumptions for an approximating semigroup. Estimates in the $C^1$-norm, a manifold containing the state space $X_2$ of the equation, another manifold contained in $X_2$, and an invariant cone method are used for the proof. A mechanical example illustrates possible applications. (Joint work with Jaqueline Godoy Mesquita).