We consider the asymptotic behaviour of various parametric multiple imputation procedures which include but are not restricted to the ‘proper’ imputation procedures proposed by Rubin (1978). The asymptotic variance structure of the resulting estimators is provided. This result is used to compare the relative efficiencies of different imputation procedures. It also provides a basis to understand the behaviour of two Monte Carlo iterative estimators, stochastic EM (Celeux & Diebolt, 1985; Wei & Tanner, 1990) and simulated EM (Ruud, 1991). We further develop properties of these estimators when they stop at iteration K with imputation size m. An application to a measurement error problem is used to illustrate the results.