A copying-type garbage collector operates in multiple concurrent threads. Each thread evacuates potentially reachable objects from the from space to the to space in a depth-first manner: if a thread has evacuated an object containing references to any from-space objects, it evacuates all of that object's descendants before it evacuates any other reachable objects. To keep track of descendants that must be evacuated before non-descendants can be, the thread places objects containing references to non-evacuated objects into a linked list maintained by pointers that it installs in the from-space locations from which the objects on the list were evacuated. Additionally, it divides the to space into local-allocation buffers ("LABs") to which respective threads exclusively evacuate objects, and each thread maintains a LAB stack representing all the LABs it has filled that still contain references to unevacuated from-space objects. When a thread has completed evacuating the descendants of evacuees in all of its LABs, it "steals" work from other threads. It may do so, for instance, by processing a reference in an object belonging to another thread's list, by transferring to its own list one or more objects from another thread's list, or by transferring to its own LAB stack one or more LABs from another thread's LAB stack.