Noether's theorem on the connection between Noether symmetries and conservation laws of Differential equations that come from a variational principal due to Emmy Noether [Nachr. Konig. Gesell. Wissen. Gottingen, Math.-Phys. Kl., 1918] is well known. Recently Kara and Mahomed introduced a Noether type symmetry for differential equations (DEs) not necessarily stemming from a Lagrangian formulation [Nonlinear Dynamics, 45:367-383, 2006]. These Noether type operators can also be used to construct conservation laws for the DEs. The definition of Noether type symmetries of partial differential equations (PDEs) with two independent variables is generalized to include operators dependent on nonlocal (or potential) variables. These nonlocal Noether type symmetry operators can be used to generate (nonlocal) conservation laws of the PDEs. The theory is applicable to (systems of) PDEs with two independent variables, whether the PDEs result from a variational principle or not. Several examples are included to illustrate the theory.