We present here a bounded memory size Obstruction-Free consensus algorithm for the asynchronous shared memory model. More precisely for a set of n processes, this algorithm uses n+2n+2 multi-writer multi-reader registers, each of these registers being of size O(log(n))O(log⁡(n)) bits. From this, we get a bounded memory size space complexity consensus algorithm with single-writer multi-reader registers and a bounded memory size space complexity consensus algorithm in the asynchronous message passing model with a majority of correct processes. As it is easy to ensure the Obstruction-Free assumption with randomization (or with leader election failure detector ΩΩ) we obtain a bounded memory size randomized consensus algorithm and a bounded memory size consensus algorithm with failure detector.