We study order and zero-stability of two-step methods of Obrechkoff type for ordinary differential equations. A relation between order and properties of mth degree polynomials orthogonal to
x
μ
i
{x^{{\mu _i}}}
,
1
⩽
i
⩽
m
1 \leqslant i \leqslant m
, where
−
1
>
μ
1
>
μ
2
>
⋯
>
μ
m
- 1 > {\mu _1} > {\mu _2} > \cdots > {\mu _m}
, is established. These polynomials are investigated, focusing on their explicit form, Rodrigues-type formulae and loci of their zeros.