Microsoft, the world's top software company whose Windows operating system runs on 90% of the world's computers, issued patches to fix the problems as part of its monthly security bulletin. It listed both as critical vulnerabilities.
One flaw is a vulnerability in some versions of the Windows Media Player for playing music or video files.
The flaw makes it possible for an attacker to use a malicious file that controls the appearance of the player to launch other programmes on a computer.
Oliver Friedrichs, a senior manager at Symantec Corp., a leading maker of security software, said in a statement on Tuesday: "Application vulnerabilities, such as the issue in Windows Media Player, are a growing cause of concern."
Another vulnerability in some versions of Internet Explorer would make it possible for an attacker to take total control of a PC.
Last month, Microsoft issued fixes for two security flaws in Windows that could let an attacker commandeer someone's computer.
Microsoft has been working for more than three years to improve the security and reliability of its software as more and more malicious software targets weaknesses in Windows and other Microsoft software.