This work examines delta modulation systems in which statistical knowledge about the signal to be tranmitted is explicitly used in sistem design. These modulators are called here structured delta modulators. After a brief introduction to delta modulation some well-known systems are described. Structured systems are then formally defined and analytical difficulties in finding general solutions are pointed out. Starting from a system proposed by C.L. Song, general equations are derived. These equations, which are more complete than the ones obtained by Song are then specialized to first-order Gauss-Maarkov signals, leading to what has been called a modified Song modulators. Digital simulations results are then obtained for song modulators, modified Song modulators and linear delta modulators. An adptive producedure is finally suggested to improve the dynamic range of these systems.