We show that space-time resonances induce high-frequency instabilities in the two-fluid Euler-Maxwell system. This implies in particular that the Zakharov approximation to Euler-Maxwell is stable if and only if the group velocity vanishes in the Schrödinger equation satisfied by the envelope of the WKB electrical field. Our analysis further shows that time resonances may fail to induce fast instabilities, even in the case of incompatible nonlinearities, in the presence of fast transverse variations of the WKB profile. This is joint work with Eric Dumas (Grenoble) and Lu Yong (Prague).