The search for high order A-Stable numerical methods has been between implicit Rung-Kutta methods and implicit Linear multistep methods. The cost of implementation of these methods is high due to its implicitness. Explicit A-stable multistep methods will be most desirable for the treatment of non-linear Ordinary Differential equations. This study constructed a class of A-stable Block adams bashfort explicit (Babe) methods including their hybrid forms. The new methods tested on non-linear initial value problems show that they perform well and favourably compete with the Block hybrid adams moulton (Bham) methods of a higher order.