This paper is concerned with the accuracy and efficiency of the ten step blended block linear multistep method for the approximate solution of Holling Tanner Model and the Van Da Pol equations. The main methods were derived by blending of two linear multistep methods using continuous collocation approach. These methods are of uniform order eleven. The stability analysis of the block methods indicates that the methods are Aâ€“stable, consistent and zero stable hence convergent. Numerical results obtained using the proposed new block methods were compared with those obtained by the well-known ODE solver ODE15 S to illustrate its accuracy and effectiveness. The proposed block methods are found to be efficient and accurate hence recommended for the solution of stiff initial value problems.