[en] Using the method of perturbative quantization in the first order approximation, we quantize a nonlocal QED-like theory including fermions and bosons whose interactions are described by terms containing higher order space-time derivatives. As an example, the two-dimensional space-time noncommutative QED (NC-QED) is quantized perturbatively up to O(e²,θ³), where e is the NC-QED coupling constant and θ is the noncommutativity parameter. The resulting modified Lagrangian density is shown to include terms consisting of first order time-derivative and higher order space-derivatives of the modified field variables that satisfy the ordinary equal-time commutation relations up to O(e²,θ³). Using these commutation relations, the canonical current algebra of the modified theory is also derived.