High-power passive Q-switching and mode-locking operation regimes of diode end-pumped Nd:YAG, Nd:YVO4, and Nd:YAP active media, operating at a 1.34-?m wavelength are investigated with V3+:YAG crystal as the saturable absorber. The highest average power of 2.1 W results from a Nd:YVO4 crystal placed in a 70-mm-long linear cavity. The corresponding pulse peak power and width are 0.1 kW and 133 ns, respectively. Employing a Nd:YAP crystal and 35-mm cavity length, the highest peak power of ~2.8 kW results when the laser runs at a 6.5-kHz repetition rate for an average power of â€”0.4 W. A record of 79-xJ pulse energy results from a 64-mm-long resonator with Nd:YAG gain media, however, for a decreased average power of ~0.24 W and pulses of 40-ns width. The mode-locking operation regime is investigated in a Z-type cavity. The best results, namely, ~0.5 W average power with mode-locked envelope energy in excess of 30 ?J and mode- locked pulse energy of 0.7 ?J, are obtained from the Nd:YVO4 media. Trains of 1-?s-wide pulses with improved stability result from a 1.5-m- long designed cavity with KTP crystal applied for passive negative feedback. A numerical modeling that takes into account the short recovery time of V3+:YAG saturable absorber (~5 ns) and excited state absorption effect is used to analyze and obtain general rules for optimizing such lasers.