Agency很常见，即代理，代理人经本人授权以本人名义行事，本人对代理人的代理行为负责。。Agency by estoppel和agency in fact属于两种不同类型的代理。

Estoppel本质是侵权法上的概念，注重对受害人因信赖他人言辞（声明或承诺）而导致的信赖损失的保护。在这里Agency by estoppel指的是表见代理。

表见代理，也称为 agency by operation of law, apparent agency 或 ostensible agency，并不存在真正的代理关系（actual agency)，即委托人和代理人之间并无代理协议存在，只是因委托人的行为让第三人合理地认为他与代理人之间确有代理关系，且第三人因此种确认作为且受到伤害，此时由法院依据法律推定成立而委托人不得否认的一种代理关系。

Agency by estoppel is a legal term that refers to someone giving the impression to a layperson that they are an agent of another individual or company. This agency is not officially appointed and the agent by estoppel is not authorized to represent the person or company they purport themselves to be working for.

In fact则多指实际的、事实上的。如：attorney in fact事实代理人（委托人为某种特定目的授权其代理或委托其从事非法律性质的行为的人。）

相比之下，agency in fact (“事实代理”)所表示的代理关系则是由委托人和代理人经协议事实确立的，其与前者正好相对。the agency that happens where there is an agreement between the agent and the principal.

以下为相关双语例句，供参考：

Agency by estoppel means that a defendant will be liable to a plaintiff because the defendant’s negligence caused the plaintiff to reasonably rely on there being an agency relationship between the defendant and someone who purported to act on behalf of the defendant.

根据表见代理，因被告疏忽而导致原告合理依赖被告与声称代表被告行事的人之间存在代理关系的，被告将对原告承担责任。