The article explores the relationship between two types of causality in spacetime: Hawking's stable causality and Sorkin and Woolgar's K-causality. The researchers show that a spacetime is stably causal if the Seifert causal relation is a partial order. They also demonstrate that in a K-causal spacetime, widening light cones around an event doesn't affect K-causality. However, they couldn't fully prove the equivalence between the two types of causality. It is proven that if K-causality equals stable causality, the K+ future matches the Seifert future in any K-causal spacetime. Examples are given where the K+ future differs from the Seifert future in causal spacetimes.