Rdio this morning announced that its on-demand music subscription and discovery service is now available to users in Spain and Portugal.

For the US-based startup, which was created by Skype and Kazaa founders Niklas Zennström and Janus Friis, this marks its second and third expansion to Europe after debuting in Germany in January 2012.

It also means Rdio is entering a country where Spotify – arguably its main rival globally – is available after the latter’s (late) debut in the United States, where Rdio had been available long before Spotify.

For the record, the free version of Spotify is available in Spain but not (yet) in Portugal, although I gather Portuguese citizens with credit cards or PayPal accounts can sign up for the premium version.

Rdio is now available in the US, Canada, Brazil, Germany, Spain, Portugal, Australia and New Zealand. In the launch blog post, the company notes that “this is just the beginning”.

The service lets users access a catalog of roughly 12 million songs, charging €4.99 per month for Web-only access and €9.99 per month for Unlimited (Web and mobile) access.

Rdio is available on the Web, Mac and PC desktops, the iPad, iPod touch, loads of smartphones (iPhone, Android, BlackBerry, Windows Phone 7) and at home in the Sonos wireless audio system.