In inflationary scenarios with more than one scaler field, inflation m
ay proceed even if each of the individual fields has a potential too s
teep for that field to sustain inflation on its own. We show that scal
ar fields with exponential potentials evolve so as to act cooperativel
y to assist inflation, by finding solutions in which the energy densit
ies of the different scalar fields evolve in fixed proportion. Such sc
aling solutions exist for an arbitrary number of scalar fields, with d
ifferent slopes for the exponential potentials, and we show that these
solutions are the unique late-time attractors for the evolution. We d
etermine the density perturbation spectrum produced by such a period o
f inflation, and show that with multiple scalar fields, the spectrum i
s closer to the scale-invariant than the spectrum that any of the fiel
ds would generate individually. [S0556-2821(98)50118-X].