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system of non-linear ODEs

Hi !

Does anyone know how to solve non-linear ODE systems like 

GP ' [t] ==   a  - b GC[t] - c GP[t]  - GC' [t]
GC'[t] == d GP[t] GM[t] / (e + f GM[t] )

a,b,c,d,e  constants

with the initial conditions :

GP[0] == GC[0] == 0   GC' [0]== 0

where GM[t] can be either a constant, GP[t] or a function of GP[t] and

Mathematica DSolve bounces it back in the case GM[t] == GP[t]  and

Why ? How to solve that ?

Thanks a lot

scd at 

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