A parametric theory is developed of flux gates with an output at the fundamental frequency. General and particular design expressions were derived. Special emphasis is focussed on the effect of internal parametric amplification of the useful signal that makes possible detection and measurement of weak magnetic fields. The sources of internal flux gate noise were established and ways for their reduction are indicated. The practically achievable noise level was found to be\({{\left( {2 - 5} \right) \cdot 10^{ - 13} T} \mathord{\left/ {\vphantom {{\left( {2 - 5} \right) \cdot 10^{ - 13} T} {\sqrt {Hz} }}} \right. \kern-\nulldelimiterspace} {\sqrt {Hz} }}\).