SAN FRANCISCO — They aren’t out of the woods yet. Google Inc., Apple Inc., Adobe Systems Inc. and Intel Corp. avoided a potentially messy trial and $9 billion in damages by settling so-called no-poach litigation late last month for $324 million. But now a new round of litigation is beginning. In a series of shareholder derivative suits, plaintiffs lawyers allege executives of those tech companies harmed their companies, and in turn their shareholders, by entering into the illegal pacts.

It’s an unusual move—derivatives generally go hand in hand with securities fraud cases, not antitrust suits—and one that faces several hurdles. But plaintiffs attorneys say these Silicon Valley executives are prime targets for derivative actions.