If \(B\) is a metric space then a controlled space is a pair \((X,p)\) where \(X\) is a space and \(p : X \to B\) is a map. Generalizing a construction of D. R. Anderson, F. X. Connolly, S. Ferry and E. K. Pedersen (in preprint), the author defines a functor, called continuously controlled \(A\)-theory, which depends only on the topology of the space \(B\), not on its metric structure. The author reproves some results concerning the structure of continuously controlled K-theory of rings (resp. additive categories).