Rick Osterloh, President and Chief Operating Officer of Motorola Mobility, claps during a launch event of its new smartphone products in Beijing, January 26, 2015. Motorola has reinvented itself as a strong Android phone maker, and under Lenovo Group, is thriving in new markets including India, the world's third biggest smartphone market. Reuters/Stringer

There's good news on the upgrades front for users of the first-generation 2013 Moto X phone.

While some tests are currently underway, the Android Lollipop 5.1 upgrades might start rolling out in several markets, if all goes well, a Motorola Mobility executive posted on his Google+ page on Wednesday.

“I wanted to give a quick update on where we are with the Lollipop upgrades for the 2013 Moto X (1st Gen) devices,” David Schuster, senior director for software product management at Motorola, wrote. “We have started full soak testing in France and Germany retail this week with the expectation of full deployment next week if all goes well.”

In addition, Motorola has addressed an issue it found in a previous test, and expects to start testing in the U.S. and Brazil for retail markets later this week, he wrote. “If all goes well, full deployment can happen the following week.”

While Motorola is working with carriers in markets such as the U.S., where upgrades happen via “carrier channels,” it’s not clear from Schuster’s post if “full deployment” includes markets such as India, where the company’s phones -- including the cheaper Moto E and Moto G -- have garnered a loyal fan following.

However, Motorola’s India-specific website does include the first-generation Moto X as part of a portfolio of handsets included in its Lollipop upgrade rollout.