In this paper we shall prove some fixed and periodic point theorems for the mapping $H\colon S\to S$ where the triplet ($S,\mathcal F,T$) is a probabilistic Menger space with continuous $T$-norm $T$ such that the family $\{T_n(x)\}_{n\in N}$ is equicontinuous at the point $x=1$, where: \[ T_n(x)=\underbrace{T(T(\dots T(T}_{n-ext{time}}(x,x),x),\dots,x),\qquad xı[0,1],\quad nı N \]