After mating, the female damselfly is ready to lay its eggs. Different species has different methods of egg-laying process. I particularly like the Heliocypha and Libellago species where the male will guard the ovipositing female from the disturbance by rival males. The entire egg-laying process usually last about 1-2 minutes. During this short period, the female would fly to different spots to lay its eggs while the male would follow closely wherever it goes.
The male of some species such as Lestes praemorsus decipiens probably feel safer guarding its female by remaining in tandem through the egg laying process.
Most damselfly species would either lay eggs above the waterline or at the waterline. The most amazing one are those that lay its eggs below the waterline such as the Dysphaea dimidiata.