Cosmological evolution driven incorporating continuous particle creation by the time-varying gravitational field is investigated. We consider a spatially homogeneous and isotropic universe with two matter fluids in the context of general relativity. One fluid is endowed with gravitationally induced `adiabatic' particle creation, while the second fluid simply satisfies the conservation of energy. We show that the dynamics of the two fluids is entirely controlled by a single nonlinear differential equation involving the particle creation rate, F(t). We consider a very general particle creation rate, F(t), that reduces to several special cases of cosmological interest, including F = constant, F proportional to 1/H^n (n an integer N), F proportional to exp(1/H). Finally, we present singular algebraic solutions of the gravitational eld equations for the two-fluid particle creation models and discuss their stability.