  We study systems of stochastic differential equations describing positions
x_1,x_2,...,x_p of p ordered particles, with inter-particles repulsions of the
form H_{ij}(x_i,x_j)/(x_i-x_j). We show the existence of strong and pathwise
unique non-colliding solutions of the system with a colliding initial point
x_1(0)\leq ...\leq x_p(0) in the whole generality, under natural assumptions on
the coefficients of the equations.
