Depends on how you define they are marketing to your clients.  I would have an adult conversation, expressing my concerns.  If the other agent didnt see what they are doing is wrong, then off to the broker for another conversation.  Good luck.

You need more specifics in your question like how they obtained your database?  Are they specifically targeting your contacts or blanket marketing that just happened to reach your clients?  Talk to your broker.  If you don't like the atmosphere within your office and the broker isn't willing the resolve your issue(s), it might be time to make a change.

Did they steal your database? If they did then you have a serious problem. If they have made contact at some point with the same people I would say they have the right to do it too. They are not just your contacts other companies may also be marketing to them. What makes you think it should be hands off?

Is he or she stealing the contac info off your desk? I would report them to your managing broker and if nothing is done look for another venue to hang your license. 

You need to up your game.

Unless you are engaged in a CONTRACT with a citizen, they are fair game to every agent, using every means, at every opportunity to distract your list from what you have to offer. This means those on your birthday calendar, all of your family members, those you send newsletters to, even the ones whose baby you may have kissed.

Focus your building relationship and marketing to align with your business goals where you are providing a distinctive service to a very identifiable population.

The marketer (agent) who does the best job, using the resources they choose to use, will win.  The score is not tallied by who you mail to, but who calls you. Keep your eye on the goal. If they don't call you, don't blame it on the competition.

Man to man talk!

AR followers: I appreciate your response! This is what makes AR the community it is! My professional stance is that if you are aware of a relationship between someone in your office and a client, be respectful of that, and do not cross your boundaries. Its equivalent to going behind someone's back and being greedy. My partner in the office tells me when I call certain real estate companies, who he is already working with and out of respect I do not market to those individuals.

Be careful about who you work with because unfortunately there are some people who cross boundaries with things like marketing to prospective or existing clients. In regards to comments below, I definately am a firm believer that if your relationship is strong and stands out above others it is that which will become noticable and your clients will support you in the end.

Talk to yor Broker with that other agent at the same time.

If they are loyal to you, or have an exclusive agency relationship, there should be no issue.   If your client is willing to send a note to this agent advising them that you are there Realtor, that should help.

You can mention something to the other agent, though in most cases this isn't productive.

Provide good service to your "contacts," and they will seek your advice in real estate matters.

Here in Arkansas if you do have the agreement in writing the clients are free game.  Once that agreement is in writing it's a whole new ballgame. 

You do not own contacts and you will always have competition. 

Your written exclusive agreements will give you the best protection.