This　paper　presents　the　circuit　design　and　magnetic　integration　of　push-pull　class-E　inverters　for　wireless　power　transfer　(WPT)　up　to　megahertz.　The　design　criterion　for　achieving　zero-voltage　switching　(ZVS)　of　a　class-E　inverter　with　coupled　windings　is　derived　mathematically.　The　approaches　of　magnetic　integration　for　push-pull　class-E　inverters　are　analyzed　and　compared.　Then,　a　new　magnetic　structure　with　hybrid　magnetic　materials　is　proposed　to　build　the　integrated　inductors　with　either　coupled　windings　or　uncoupled　windings.　A　3-MHz　WPT　system　is　built　to　verify　the　analysis.　The　detailed　comparison　of　the　class-E　inverters　with　magnetic　integration　is　presented　in　terms　of　switch　voltage,　efficiency,　harmonic　currents,　and　thermal　distribution.　In　the　optimized　design　example,　the　switches　keep　ZVS　over　the　entire　load　range　without　using　any　closed-loop　control.　The　system　efficiency　reaches　87.1%　at　350-W　output　power.