We investigate the application of the acceleration technique known as Iterated Defect Correction (IDeC) for the numerical solution of singular initial value problems of the form

z'(t)=M(t)/t z(t)+f(t,z(t)), t∈ (0,1],	(1)
B0z(0)=β,	(2)
z ∈ C[0,1].	(3)

where B₀ and β are suitably chosen to yield a well-posed problem. We show that IDeC based on the implicit Euler method performs satisfactorily while for higher order methods like the box scheme or the trapezoidal rule, order reductions occur. This is due to the break-down of the asymptotic expansions of the global error caused by the singularity. Also, a comparison with extrapolation methods is made. Moreover, we explain why IDeC does not work in general for terminal value problems of the form

z'(t)=M(t)/t z(t)+f(t,z(t)), t∈ (0,1],	(4)
B1z(0)=β,	(5)
z ∈ C[0,1].	(6)

Experimental results are presented in order to support and illustrate the theory.