Summary: A Turing machine multiplies on-line if it receives its inputs low order digits first and it produces the \(k\)-th output digit before reading in the \((k+1)\)-st inputs. We present a general method for converting any off-line multiplication algorithm which forms the product of two \(n\)-bit binary numbers in time \(F(n)\) into an on-line method, and the new algorithm requires time only \(O(F(n) \log n)\). Applying this technique to the fast multiplication algorithm of A. Schönhage and V. Strassen [Computing 7, 281–292 (1972; Zbl 0223.68007)] gives an upper bound of \(O(n (\log n)^2 \log \log n)\) for on-line multiplication of integers. Other applications are to the on-line problems of products of polynomials over a finite ring, recognition of palindromes, and multiplication by a constant.