The Painlevé analysis is conducted on the 2 + 1 dimensional equations of the type of derivative NLS and of Three-Wave Interactions. We find in the first case that certain pseudo appearance of logarithmic terms may be alleviated in the Painlevé test, while in the second case we show that the multiorder resonances at index zero for vector equations may co-exist with the Painlevé property. Both cases are thus shown to pass the WTC Painlevé test.