Yes, according to the principles of special relativity, if two astronauts are traveling at speeds close to the speed of light in opposite directions and pass by each other, they will observe time dilation effects and perceive each other's aging processes to be slower compared to their own.
This phenomenon is known as the twin paradox, a thought experiment commonly used to illustrate the concepts of time dilation and relativistic effects. In the twin paradox scenario, one twin remains on Earth while the other travels at high speeds through space and then returns. Due to the difference in their relative velocities, the traveling twin will experience time passing more slowly than the twin on Earth.
In the scenario you described, where two astronauts are traveling in opposite directions, both astronauts will perceive the other's clock to be running slower. This means that each astronaut will observe the other aging more slowly than themselves.
However, it's important to note that this effect is reciprocal. Both astronauts will view the other as experiencing time dilation, and each will think they are "aging slower" compared to the other. When they reunite after their journeys, they will find that they have aged differently from each other.
It's worth mentioning that these effects become more significant as the relative velocity between the two observers approaches the speed of light. Additionally, the time dilation effects are experienced by the observers themselves, so from their own perspectives, they perceive time passing normally while observing the other as experiencing time dilation.