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From 2-Spyware.com
MWSOEMON.EXE description:
This is a part of an adware application, published by WebSearch. This program displays commercial advertisements, adds an additional toolbar to Microsoft Internet Explorer web browser, but also can block certain web sites and change various browsing settings. File mwsoemon.exe provides several extra functions to Outlook Express mail program. It doesn't harm a computer, but along with the adware can violate user's privacy. It is recommended to uninstall the adware and remove all its components.
In other words, it is a part of MyWebSearch software (usually it is the MyWebSearch toolbar with certain add-ons). Although this program was classified as adware, it is not malicious. It is up to you to decide whether you need it or not.