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The author is concerned with the equation u +u = g(u, p) + μf(t), where p, μ are small parameters, f is an even, continuous π - periodic function, g is an odd smooth function of u, such that g(u,p) = O ( Ι pu Ι+ Ι u³ Ι), as p and u go to zero. The main results are that, under certain conditions, the small 2π - periodic solutions maintain some symmetry properties of the forcing function f(t), when μ≠O. Some other interesting results describe the variation of the number of such solutions as p and μ vary in à small neighbourhood of the origin. The author uses the approach of Alternative Problems.