Possessiveness in LGBT relationships

I am now entering second year in my first lesbian relationship. Once I entered it, I found that I was more possessive (not jealous, just possessive) of my partner, an experienced lesbian, than I was with any man that I had ever been with. I also noticed that she was more possessive of me, again, than any man that I had been with. I dared to bring this up, and she said that this was very typical with lesbian relationships.

What are your feelings about this?