A procedure employing stochastic B-series is used to determine the order of strong and of weak convergence of implicit stochastic Runge-Kutta (SRK) methods that utilize an iterative scheme to compute internal stage values. The results apply to SRK methods for stochastic differential equations of the Ito type and of the Stratonovich type. Summaries of numerical results for three examples verify the accuracy of the theory’s prediction of the number of iterations needed to achieve a given order of convergence.