This page applies only to older versions of the framework (v0.x). In v1.x and higher, both agents and tools are asynchronous by default, and tool-level parallelism is configured via ModelSettings.parallel_tool_calls and/or per-tool one_call_at_a_time.
Asynchronous execution allows you to run your agents or tools asynchronously in separate threads. This can be useful for shortening response times for certain I/O-bound tasks.

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Async Agents

To run each agent in a separate thread, you need to use a special SendMessageAsyncThreading tool class. See Custom Communication Flows for more information. 
from agency_swarm import SendMessageAsyncThreading
from agency_swarm import Agency

agency = Agency(agents=[ceo], send_message_tool_class=SendMessageAsyncThreading)
With this mode, the caller agent does not receive an immediate reply. Instead, it first gets a system notification confirming that the message has been sent to the recipient agent. Later, the calling agent can retrieve the actual response from the recipient.

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Async Tools

To run each tool in a separate thread, you need to adjust the ToolConfig class for each tool that you want to run asynchronously. See Custom Tools Configuration for more information. 
from agency_swarm import BaseTool

class Tool(BaseTool):
    # ...

    class ToolConfig:
        async_mode = "threading"

    # ...
With this mode, the agent will still have to wait for the tool to finish before it can continue with the next step in the conversation. So, it only makes sense to use this mode with multiple tools for the same agent that are not dependent on each other.