  Parity-time ($\cal PT$) symmetric lasers have attracted considerable
attention lately due to their promising applications and intriguing properties,
such as free spectral range doubling and single-mode lasing. In this work we
discuss nonlinear modal interactions in these laser systems under steady state
conditions, and we demonstrate that several gain clamping scenarios can occur
for lasing operation in the $\cal PT$-symmetric and $\cal PT$-broken phases. In
particular, we show that, depending on the system's design and the external
pump profile, its operation in the nonlinear regime falls into two different
categories: in one the system is frozen in the $\cal PT$ phase space as the
applied gain increases, while in the other the system is pulled towards its
exceptional point. These features are first illustrated by a coupled mode
formalism and later verified by employing the Steady-state Ab-initio Laser
Theory (SALT). Our findings shine light on the robustness of single-mode
operation in these lasers against saturation nonlinearity in $\cal
PT$-symmetric lasers.
