This paper analytically investigates the effects of system and controller parameters and operating conditions on the dynamic and transient behavior of wind turbines (WTs) with doubly-fed induction generators (DFIGs) under voltage dips and wind speed fluctuations. Also, it deals with the design considerations regarding rotor and speed controllers. The poorly damped electrical and mechanical modes of the system are identified, and the effects of system parameters, and speed/rotor controllers on these modes are investigated by modal and sensitivity analyses. The results of theoretical studies are verified by time domain simulations. It is found that the dynamic behavior of the DFIG-based WT under voltage dips is strongly affected by the stator dynamics. Further, it is shown that the closed loop bandwidth of the rotor current control, rotor current damping, DFIG power factor and the rotor back-emf voltages have high impact on the stator modes and consequently on the DFIG dynamic behavior. Moreover, it is shown that the dynamic behavior of DFIG-based WT under wind speed fluctuation is significantly dependent on the bandwidth and damping of speed control loop