In classic theorems, when we have a stochastic differential equation of the form dX t = f(t,X t )dt + G(t,X t )dW t , X t = ξ, t o ≤ t ≤ T < ∞, where W t is a Wiener Process and ξ is a random variable independent of W t -Wt o for t ≥ t o in order to have existence and uniqueness of solutions it is supposed the existence of a constant K such that: (Lipschitz condition) for all t ϵ [t o ,T], x,y ∈R d , |f(t,x)-f(t,y)| + |G(t,x)-G(t,y)| ≤ K|x-y|· And for all t ∈|t o ,T | and x ∈ R d , |f(t,x)| 2 +|G(t,x)| 2 ≤ K 2 (1+|x| 2 ). In this article we prove an existence theorem under weaker hypothesis: we require only that f and G be continuous in the second variable and the existence of a function m ϵ L 2 [t o ,T] such that |f(t,x)|+|G(t,x)| ≤ m(t) for alI t ∈ [t o ,T] and x ∈ R d .