Traveling to US with british children

Hi everyone,
 I am an american citizen and also a UK resident. I have lived in England for about 6 years now. My husband is british and we have two children together who were born in England.. I have not applied for their reports of birth abroad to the US embassy yet but they do hold UK passports. We are thinking of traveling to the US sometime next year. Are they ok to travel under a UK passport to the US even if I havn't applied for their US Citizenship?

No, they need to enter the US on a US passport as they are automatically US citizens even though you haven't registered them.

As they are American citizens already, they need their American passports to travel to the US. People have taken dual citizen children to the US on non-US passports, but it isn't recommended.