We extend earlier work of Waldhausen which defines operations on the algebraic $K$-theory of the one-point space. For a connected simplicial abelian group $X$ and symmetric groups $��_n$, we define operations $��^n \colon A(X) \rightarrow A(X{\times}B��_n)$ in the algebraic $K$-theory of spaces. We show that our operations can be given the structure of $E_{\infty}$-maps. Let $��_n \colon A(X{\times}B��_n) \rightarrow A(X{\times}E��_n) \simeq A(X)$ be the $��_n$-transfer. We also develop an inductive procedure to compute the compositions $��_n \circ ��^n$, and outline some applications.

Revision corrects typographical errors, corrects some omissions, replaces quoted (long) definitions with specific references to literature, and reorganizes material appropriately