The ambiguous command arrangements during various military operations, particularly in World War II and the Vietnam War, significantly affected relations between Australian and American commanders. Here are some key points to consider:

1. Command Structure: The command arrangements often lacked clarity, leading to confusion about authority and responsibility. For instance, during World War II, the Australian forces were integrated into the American command structure, but the exact nature of this integration was sometimes unclear. This ambiguity could lead to friction, as Australian commanders were sometimes unsure about their autonomy and decision-making power.

2. Cultural Differences: The differing military cultures and operational philosophies between Australian and American forces contributed to misunderstandings. Australian commanders often valued a more decentralized approach, while American commanders typically favored a more centralized command structure. This difference could lead to tensions, especially when quick decisions were needed on the battlefield.

3. Operational Coordination: Ambiguous command arrangements could hinder effective operational coordination. For example, during the Vietnam War, the lack of clear command lines sometimes resulted in miscommunication and operational delays. This was particularly evident in joint operations where Australian and American forces needed to work closely together.

4. Political Implications: The command arrangements also had political ramifications. Australian leaders were concerned about maintaining national sovereignty and the perception of being subordinate to American command. This concern sometimes led to reluctance in fully committing Australian forces to operations led by American commanders, which could strain diplomatic relations.

5. Joint Exercises and Training: To mitigate some of these issues, both nations engaged in joint exercises and training programs aimed at improving interoperability and understanding between their forces. These efforts were crucial in building trust and improving communication, although the underlying command ambiguities remained a challenge.

In summary, the ambiguous command arrangements between Australian and American commanders often led to operational challenges, cultural misunderstandings, and political concerns, which could strain relations. Efforts to improve communication and joint training were essential in addressing these issues, but the complexities of command structure continued to influence their military collaboration.