The nonlinear nonlocal singularly perturbed problems for the disturbed evolution equations are studied. Using the singular perturbation method, the structure of solution to the problem is discussed in the cases of two small parameters. Under the suitable conditions, firstly, the outer solution to the boundary value problem is given. Secondly, the variables of multiple scales are introduced to obtain the boundary layer corrective terms for the solution. Then the stretched variable is applied to the boundary neighborhood to get the initial layer correction term. Finally, using the fix point theorem, the uniformly valid asymptotic expansion of the solution to the problem is proved. The proposed method possesses the advantages of convenient use and high accuracy.