A spokesperson for Telstra said there had been an increase in traffic as result of the fast-spreading worm but recent upgrades to Bigpond's e-mail system had successfully absorbed its impact.
Last October, Bigpond faced a barrage of criticism and legal threats from its customers after suffering lengthy delays when using the ISPs e-mail service.
Telstra called on its users to be patient laying the blame for service problems at the feet of the Swen virus. The company said that it struggled as the virus caused an "unprecedented" surge in traffic through the BigPond ISPs e-mail servers.
Telstra's claim was supported by some Internet security companies, but sceptics observed that the e-mail service had not been affected by more prolific mass mailing worms such as Sobig and Code Red.
"The Swen virus and consequent 'spike' in e-mail of about 25 percent was unheralded and without precedent," said BigPond managing director, Justin Milne. "We are building substantial extra capacity into our e-mail systems and will continue to expand this capacity so we can be sure that we can cope with this kind of event if it ever occurs again."
However, as global e-mail systems grapple with what security experts report is the worst mass mailing worm ever, Telstra said its systems were "coping well".
Security experts have analysed two variants of MyDoom -- designed to initiate attacks on Microsoft and SCO -- and estimate that it could have been responsible for between 20 and 30 percent of global e-mail traffic over the last 48 hours.
Telstra has set aside AU$100 million to upgrade its e-mail system and so far it has increased its capacity by 70 percent and added new anti-virus features to its offering.
A spokesperson for Telstra said that the carrier's e-mail data volume requirements had doubled year-on-year every year for the last four years.