Abstract : In a distributed system, different processes synchronize in order to solve a global computation. The difficulty comes from the fact that a process does not know the other inputs. We consider here asynchronous systems: no assumption can be made regarding the relative speeds of processes. We also consider that processes can crash, i.e. stop their execution at an arbitrary point of their code. In the theoretical study of distributed systems, problems have to be considered according to two aspects: safety and progress. Safety defines whether a given value can be output. Progress defines under which conditions a process is required to terminate its operation, regardless of the value it outputs. This thesis is about the links between calculability and progress conditions of shared objects. We start by introducing and studying the notion of asymmetric progress conditions: progress conditions that don't necessarily impose the same requirements for different processes. We then study the possibility of supplying processes with abstractions in a given model. The issue of the equivalence of system models is then raised, especially when processes have access to strong objects. Finally, the thesis studies colored tasks. It presents a renaming algorithm that terminates if contention gets below a given threshold. It then introduces a new class of colored tasks that allows to unify in a single framework different problems which were previously studied independently.