Hollywood tech company J2 Global Inc. continued its expansion beyond its core Internet faxing services last week with the acquisition of a business cloud software company.

Landslide Technologies Inc., a Boston company that provides customer management software for small to medium-size businesses, will give J2 a broader offering of cloud services.

It’s the second company with cloud software that J2 has purchased since the beginning of the year. The other, Backup Solutions LLC, is a Phoenix provider of online backup software.

Hemi Zucker, J2’s chief executive, said the most recent acquisition will expand the company’s cloud business.

“The Landslide acquisition reflects continued execution of our plan to expand our array of cloud-based services for business,” Zucker said in a statement.

The company did not disclose terms of the deal. Investors responded favorably to the acquisition. Shares rose 6 percent, or $1.79, for the week to close at $29.83 on Feb. 8.

J2 was founded in 1995 as a communication services company. Its core products for many years have been online faxing software eFax and online voicemail software eVoice.

But the company has been expanding into markets other than the telephone number-centric services. It recently added e-mail marketing, data backup and hosted e-mail to its offerings.

In December, the company changed its name from J2 Global Communications to J2 Global to reflect the new business outlook.

Zucker predicted that revenue for the company’s online backup and e-mail services would reach $20 million last year, up from $8 million in 2010.

In November, J2 reported third quarter revenue of $86 million, up from $62.8 million in third quarter 2010, and net income of $25.5 million, up from $19.8 million. The company is scheduled to report fourth quarter and annual earnings Tuesday.