Is it normal to want sex, after sex, after sex?

Since my early teens I've had a very active sex drive. This doesn't mean I was sexually active with partners, but I did masturbate daily. This daily habit did satisfy my cravings, and it came to the point where I depended on masturbation to be able to sleep during the night. I also recall waking up in the middle of the night a couple of times having a random orgasm, without having dreams related to sexual activity.

Now that I am older, I have become sexually active with partners. Even though at times after intercourse I feel satisfied, only minutes or hours later I feel the need to redo. A couple of days ago, I had a intercourse, I begged my partner to have intercourse a second time, yet as soon as I got home I felt the need to masturbate. I ignored the need, but the next day it was inevitable to do so, and I did it twice before going to work.

It may sound as though it interferes with my life, but I don't feel as though it does. But I've realized that putting experiences one behind the other seems compulsive, specially thinking that I've spent years masturbating every night. The only moment I felt lack of sex drive was when I ended a serious relationship.

Is this normal??