We report measurements of the inclusive production of heavy quarkonium states in Z decays based on the analysis of 3.6 million hadronic events collected by the L3 detector at LEP. The measurement of inclusive J production and an improved 95% confidence level upper limit on Υ production are presented. In addition, two independent measurements of the ratio, fp , of prompt J mesons to those from B decay are made using two different isolation cuts to separate prompt J mesons from J mesons produced in the decays of b hadrons. The results are: <math><mtext>Br</mtext><mtext>(</mtext><mtext>Z</mtext><mtext>→</mtext><mtext>J</mtext><mtext>+</mtext><mtext>X</mtext><mtext>)=(3.21±0.21</mtext><mspace sp="0.4" width="2px" linebreak="nobreak" is="true"></mspace><mtext>(stat.)</mtext><mspace sp="0.4" width="2px" linebreak="nobreak" is="true"></mspace><msup><mi></mi><mn>+0.19</mn></msup><msub><mi></mi><mn>−0.28</mn></msub><mspace sp="0.4" width="2px" linebreak="nobreak" is="true"></mspace><mtext>(sys.)</mtext><mtext>)×10</mtext><msup><mi></mi><mn>−3</mn></msup></math>, Br(Z→ϒ(1S)+X)<4.4×10−5, <math><mtext>f</mtext><msub><mi></mi><mn><mtext>p</mtext></mn></msub><mtext>=(7.1±2.1</mtext><mspace sp="0.4" width="2px" linebreak="nobreak" is="true"></mspace><mtext>(stat.)</mtext><mspace sp="0.4" width="2px" linebreak="nobreak" is="true"></mspace><mtext>±1.2</mtext><mspace sp="0.4" width="2px" linebreak="nobreak" is="true"></mspace><mtext>(sys.)</mtext><mspace sp="0.4" width="2px" linebreak="nobreak" is="true"></mspace><msup><mi></mi><mn>+1.5</mn></msup><msub><mi></mi><mn>−0.8</mn></msub><mspace sp="0.4" width="2px" linebreak="nobreak" is="true"></mspace><mtext>(theo.)</mtext><mtext>)×10</mtext><msup><mi></mi><mn>−2</mn></msup></math>.Facultad de Ciencias Exactas