Have found a great article explaining how and why adrenaline and cortisol are produces:
Demystifying Depression/The Stress System
Be sure to take a look at Figure 2: The relationship between adrenaline and cortisol. - which clarifies this text.
The effect of the stress hormones on the brain is curious and not what you might expect. The initial surge of adrenaline can make you feel good.
Just as your levels of adrenaline start coming down, so rises the amount of cortisol flowing through your veins. Moreover, cortisol has a much larger momentum than adrenaline, which means that even though it builds up slowly, it also takes a long time to go back to normal. And should you constantly be engaging in activities which require adrenaline, so will your levels of cortisol slowly increase. In a sense, you can think of cortisol as a measure of the weighted average of your recent levels of adrenaline. I have tried to capture this feature in Figure 2.
Together with the rise of cortisol and the decrease of adrenaline, come the nasty side-effects of the stress hormones. It is at this moment that you feel bad, anxious, and having lots of negative thoughts. And this is perhaps one of the critical features of stress which flies against common sense: you only feel its bad aspects when your body is stressing down and progressing towards a more relaxed state. When you are building up on adrenaline, in effect stressing up, you might even be feeling good! This explains what is popularly known as the adrenaline rush and the consequent adrenaline crash.
Having too much cortisol flowing through your veins has another nasty side-effect: the recovery time from any adrenaline surge increases. In a sense, the relation between adrenaline and cortisol goes both ways: the adrenaline curve influences the cortisol curve, and vice-versa. Figure 3 tries to capture this reaction effect by showing the adrenaline response curve for three individuals subjected to the same physical exercise. Notice how the more serious the depression (which translates into higher levels of cortisol, as you will soon understand), the longer it takes for the body to go back to normal.