What is the doctrine called where either party employer or employee may terminate his her employment relationship at any time and for any reason?

Overview

At-will employment refers to an employment agreement stating that employment is for an indefinite period of time and may be terminated either by employer or employee. If an employment is at-will, such an agreement would typically be expressly included in the relevant employment contract. 

Exceptions

Even if an employment agreement contains an at-will provision, there are certain reasons as to why termination could still be wrongful. These exceptions will typically vary by state.

Public Policy Exception

The public policy exception bars an employer from terminating employees in violation of well-established public policy of the state. As an example, in many states an employee may not be terminated for filing a workers' compensation claim after an on-the-job injury.

Many states do not allow employers to terminate employees for refusal to violate the law at the employer's request.  Criteria for what violates public policy in a particular state varies from state to state. 

Implied Contract Exception

The implied contract exception means that an employee may have an expectation of a fixed term or even indefinite employment based on something the supervisor has done. This can take the form of employer's statements, an employer’s practice of only firing employees for cause, or an assertion in the employee handbook that specific termination procedures will be followed.

Implied Covenant of Good Faith and Fair Dealing

Some states recognize an implied covenant of good faith and fair dealing in employment relationships. Under this exception, an employer typically may not terminate an employee in bad faith or terminate an employee when the termination is motivated by malice.

Further Reading

For more on the at-will employment doctrine, see this Nebraska Law Review article, this Florida State University Law Review article, and this Monthly Labor Review article.

What is the term for an employment relationship where an employer or employee can terminate the relationship at any time and for any reason?

C-Level Law Employment in the United States is generally “at-will,” meaning that the employee and employer both have the right to terminate the employment relationship at any time, without prior notice, for any reason or no reason.
Employment at will. - is a legal doctrine that specifies that employment may be terminated by either the employer or employee for any reason.

What is the doctrine that states that employers may not fire?

Fast facts about the at-will employment doctrine In the most basic sense, at-will employment means that an employer can terminate an employee for almost any reason — although a few exceptions to the rule may exist under state and federal law.

Which doctrine provides employers the right to terminate or hire or transfer employees at any time as long as doing so is not illegal?

Employment-at-will is legal protection for employees and employers to be able to end employment at any time, for any reason, except for illegal reasons. At-will means according to the desire, for no other reason.