You don't supply nearly enough info for us to help you. Is there something you can do on your property to address any adverse drainage/erosion problems before they occur? What exactly is the erosion issue--is his property elevated higher than yours, is it a cliff or high bank that might come tumbling into your living room, how large/old are the trees and why is he removing them, could the trees be causing problems on his property?
I think you should do all you can on your own property to make sure it is stable. After all, your neighbor is not responsible for protecting your property no matter what the local ordinances or laws may say. Take responsibility for yourself and your belongings. Put in a drainage channel along the property line if necessary, plant a few trees for windbreak. It is your property. I'm sure your neighbor is not sitting in his house thinking of ways to make your life miserable. More likely than not, he is already aware of drainage/erosion issues and is making plans to address this.
I don't know when we all became so intolerant and controlling in this country. My neighbors can do whatever the hell they want and it is my responsibility to make sure my property is safe by using retaining walls, plantings, or whatever else is necessary for my quiet enjoyment of my property. Try a little live and let live. We will all be a better off for it. I have a hard time believing this is a problem that two adults can't handle without getting courts involved.
The cost of litigation in this country has made actual neighborhoods a thing of the past. We just sue each other if we can't get our way and neighbors living a few hundred feet from each other never get to know each other. They pull into their garages, close the door, and that is the end of it. Do you really want to live that way? Because of all these nuisance suits, I am stuck living with government telling me what I can and can not do at every step of the way. Permits are required for everything and common sense has become a rare bird indeed.
So plant a windbreak, put in some erosion control and invite your neighbor over for a nice dinner this week. You will not only improve your own life, you will improve mine as well. Thanks.
ps- Perhaps your situation is more dire than I know and if that is the case than I appologize for my harsh words. Some neighbors can be thoughtless and difficult to live with and legal action may be necessary. I hope that this is not the case in your situation.