Hi PedroAM,
I had both anxiety and depression last year, and now mainly only anxiety. Both can be together, or can induce the other. If you are mainly depressed, but have anxiety developed out of this, that is very common. It is also common to have anxiety, and have depression as a symptom of being anxious in certain situations or hopeless that the anxiety isn't going away or that it won't get better in the future. I was told that depression thought patterns are mainly rooted in the past - hopeless about what happened, how life came to be this way, etc. - and anxiety thought patterns are mainly rooted in the future - uncertain of what will happen, hopeless about nothing getting better or ever changing, etc.
Either way, as separate entities on their own, or as a condition of the other, both anxiety and depression can be present, and can make it that much more difficult to recover. Dealing with both sets of symptoms right away with proper coping mechanisms, treatment (therapy and/or medication), and a lot of practice and hard work will help overcome both depression and anxiety and can lead to a full and fulfilling life.