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In the first chapter of this work, the retarded functional differential equations x(t) = - λx(t) + λf(x(t - 1)) are studied. We show the existence of an unbounded continuun of slowly oscillating periodic solutions that bifurcates from a non zero equilibrium. In Chapter II, we apply the results of the first chapter in three mathematical models used in Biology; In the last part we study the stability of the equations x(t) = - λx (t) + f(g(t - R₁), x(t - R₂),...,x(t - R_k)) where x ε R and f: Rⁿ → R. Some results that are independent of the size of the delays are established.