These last three decades, many second order (SO) and higher order (HO) high resolution (HR) direction finding (DF) methods, such as 2q-MUSIC (q ≥ 1), exploiting the information contained in the SO or HO circular (C) cumulants of the data, have been developed. However, for 2qth-order non-circular (NC) sources such as M-PSK sources with M ≤ 2q, strong gains in performance may be obtained by taking into account the information contained in both 2qth-order C and NC cumulants of the data, giving rise to NC 2qth-order DF methods. Numerous NC DF methods have been developed these last fifteen years but mainly at the SO and under restrictive assumptions on the sources. The purpose of this paper is to give new insights into NC 2q-MUSIC methods for 1 ≤ q ≤ 2 and for arbitrary NC sources.