We examine the potential contamination of cometary nuclei through impacts from asteroidal origin meteoroids. The paper uses a simple model and has the goal of determining whether asteroidal contamination is potentially significant. We assume a meteoroid power law mass distribution with index values in the range from s=1.83 to s=2.09. We used maximum and minimum models which we believe will bracket the true meteoroid mass distribution. We identify those comets which are expected to be most significantly contaminated, and find values of up to 3.6 kg of asteroidal meteoroid impact per square meter of the cometary surface per orbital revolution. This is less than the expected mass loss per perihelion passage for most comets. Therefore any remnant effects of the contamination will depend on the penetration depth of the meteoroids in the cometary nucleus, and possibly on the distribution of active and inactive areas on cometary nuclei. We present a simple model which suggests that even small meteoroids will embed relatively deeply into a cometary nucleus.