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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(x(t-R_{1), x(t-R2), ..., x(t-Rk)) where x ∈ R and f:Rⁿ → R. Some results that are independent of the size of the delays are established.}