  We prove a version of a Nullstellensatz for partial exponential fields
$(K,E)$, even though the ring of exponential polynomials $K[X_1,\ldots,X_n]^E$
is not a Hilbert ring. We show that under certain natural conditions one can
embed an ideal of $K[X_1,\ldots,X_n]^E$ into an exponential ideal. In case the
ideal consists of exponential polynomials with one iteration of the exponential
function, we show that these conditions can be met. We apply our results to the
case of ordered exponential fields.
