They are both important. A learner must concetrate on both accuracy and fluency equally in order to achieve a standard level of English mastery. The important thing is that you need to create a balance between the two of fluency and accuracy. "Not fluency" OR "accuracy" but "fluency" AND "accuracy" To Jenny C: A person speaking a lot of broken English is not fluent! To LILIYA: You should make a discussion about this question :)

definitely " fluency"

Fluency allows you to communicate with people, but accuracy allows you to be clearly "understood" by people (and get responses that don't, necessarily, shock you).