In the field of dual three-phase permanent magnet synchronous motors (DTP-PMSMs), research on current harmonic suppression has mainly focused on steady-state operations, with limited attention given to transitional conditions such as load variations and speed adjustments. To address this gap, this article presents a strategy for harmonic suppression in DTP-PMSMs using generalized integrator (GI)-based complex current controllers. It begins by analyzing the harmonic voltage sources and the closed-loop complex harmonic admittance in DTP-PMSMs, providing a clear method to evaluate suppression performance in both steady and transitional states. This article then introduces two types of GI-based complex current controllers, namely, generalized type-I (GT-I) and type-II (GT-II), discussing their design principles, parameter analysis, and implementation methods. Notably, these controllers offer easy parameter tuning and a decoupled current loop, enhancing usability and stability. Compared with existing methods, the GT-II current controller with small damping shows superior performance in handling resonance frequency deviations and adapting to transitional conditions. The feasibility and effectiveness of the proposed method are validated by the experiments on a high-speed DTP-PMSM platform.