An initial-boundary value problem of subdiffusion type is considered; the temporal component of the differential operator has the form ¿i=1¿qi(t)Dt¿iu(x,t), where the qi are continuous functions, each Dt¿i is a Caputo derivative, and the ¿i lie in (0, 1]. Maximum/comparison principles for this problem are proved under weak hypotheses. A new positivity result for the multinomial Mittag-Leffler function is derived. A posteriori error bounds are obtained in L2(¿) and L¿(¿) , where the spatial domain ¿ lies in Rd with d¿ { 1 , 2 , 3 }. An adaptive algorithm based on this theory is tested extensively and shown to yield accurate numerical solutions on the meshes generated by the algorithm.