Abstract : In the theory of approximation, the study of the rate of convergence in simultaneous approximation is an interesting areas of research. We study some approximation properties of the Durrmeyer type modification of generalized Baskakov operators introduced by Erencin (Appl. Math. Comput. 218(3):4384-4390, 2011). First, we establish a Lorentz- type lemma for the derivatives of the kernel of the generalized Baskakov operators and then obtain a recurrence relation for the moments of their Durrmeyer type modification. Next, we discuss some direct results in simultaneous approximation by these operators e.g. pointwise convergence theorem, Voronovskaja-type theorem and an estimate of error in terms of the modulus of continuity. We also estimate the error in the approximation of functions having derivatives of bounded variation. Finally, we study the rate of convergence of certain positive linear operators based on q-integers.