* Q2 revenue down 13 pct to $23.3 bln

* Q2 EPS $2.32 vs Wall Street forecast $2.01

* Raises full-year EPS to "at least $9.70" from $9.20

* Shares up as much as 3 pct in after-hours trade (Recasts, adds analysts' comment and details, updates share action)

By Ritsuko Ando

NEW YORK, July 16 (Reuters) - IBM (IBM.N: Quote, Profile, Research) surprised markets by sharply raising its full-year earnings forecast as its growing software and services businesses boosted profit margins, lifting its shares in after-hours trade.

Stock in the world's largest technology services firm rose as much as 3 percent, building on gains of more than 3 percent in the regular session, as the company's outlook and higher-than-expected quarterly earnings gave investors hope that the worst of the technology downturn may be over.

Kim Caughey, senior analyst at Fort Pitt Capital Group, was impressed by the outlook and earnings despite the lower revenue.

"This, combined with Intel's results, is pushing me to be more optimistic. Seeing they made it on the bottom line, and were pretty darned close on the top line, it gives me confidence looking at technology in general."