Lithium
Lithium burns with a strongly red-tinged flame if heated in air. It reacts with oxygen in the air to give white lithium oxide. With pure oxygen, the flame would simply be more intense.
For the record, it also reacts with the nitrogen in the air to give lithium nitride. Lithium is the only element in this Group to form a nitride in this way.
Sodium
Small pieces of sodium burn in air with often little more than an orange glow. Using larger amounts of sodium or burning it in oxygen gives a strong orange flame. You get a white solid mixture of sodium oxide and sodium peroxide.
The equation for the formation of the simple oxide is just like the lithium one.
The peroxide equation is: