Apple users have been updating their software to close a security hole which could, in theory, expose their computers to attack.
Apple Macs considered as more secure than Windows PCs
On Friday, Apple warned of a flaw in its Safari web browser which could allow malicious code to be run on a machine without a user's permission.
But security firm Secunia said there were still what it called "critical" holes in the OS X operating system.
Macs have a reputation for having fewer security problems than Windows PCs.
This is the second time this month that there have been warnings of holes in Apple's software.
'Better than most'
In a statement, Apple spoke of a "theoretical vulnerability" in its software, urging users of its OS X operating system to install a security patch.
"Apple takes security very seriously and works quickly to address potential threats as we learn of them, in this case, before there was any actual risk to our customers," said Philip Schiller, Apple's senior vice-president of worldwide marketing.
"While no operating system can be completely immune from all security issues, Mac OS X's UNIX-based architecture has so far turned out to be much better than most," he said.
Computer security firm Secunia said the patch issued by Apple did not close all the vulnerabilities in OS X.
In an advisory, it said there were still two other flaws that could allow malicious websites to run software code on a Mac.
"From the beginning, Apple has downplayed this issue," said Secunia chief executive officer, Niels Henrik Rasmussen.
"Users are still as vulnerable as Apple left them last week," he told BBC News Online.
Apple fans have long touted the benefits of the Mac, partly due to the relative immunity of the machines to the security holes and viruses that plague Windows-based computers.
Microsoft's dominance of the world of computing and its poor security record makes it an attractive target for virus writers.
Last year, Microsoft issued some 50 security bulletins about Windows. So far this year it has released 15 warnings about vulnerabilities in its software.