Stochastic linear multistep Maruyama methods (SLMMM) are constructed to numerically approximate the solution of systems of Ito stochastic delay differential equations (SDDE) of the form \[ \begin{split} X(s) l^t_0= \int^t_0 F(s, X(s), X(s- \tau_2),\dots, X(s- \tau_Q))\,ds\\ +\int^t_0 G(s, X(s), X(s-\tau_2),\dots, X(s- \tau_Q))\, dW(s),\end{split} \] where \(W\) is a standard Wiener process. Definitions of consistency, stability, root condition, and convergence are introduced, and the theory relating these concepts is developed. The theory is applied to two-step SLMMMs for a one-dimensional SDDE with one lag to obtain consistency and order of convergence. Numerical results for an example are summarized to indicate the level of error incurred in using SLMMMs.