The pilot of VH-JZU contacted Essendon Tower approaching Williamstown, requesting a clearance to enter the control zone on track to Essendon. The tower controller was unable to establish radio communication with VH-JZU and so no clearance was issued. An IFR aircraft, VH-UJV, was on descent into Essendon and communicating with Melbourne Approach Control. The Essendon tower controller noticed an unidentified aircraft entering the control zone at West Gate, on track for Essendon. He advised the approach controller and the descent of VH-UJV was stopped at 2000 feet. VH-UJV was climbed back to 2500 feet. The pilot of VH-JZU, which was the unidentified aircraft, continued to Essendon and on receiving a green light from the tower, landed. The pilot of VH-UJV was able to sight and follow VH-JZU. A loss of separation may have occurred, due to the unapproved entry into the zone by the pilot of VH-JZU. The inexperienced pilot of VH-JZU later said he thought he had received a clearance, but in hindsight realised this was a mistake on his part. When he later tried to contact Essendon Tower he could not do so but continued, thinking he had received a clearance. Significant Factors The following factors were considered relevant to the development of the incident: 1 VHF radio communication equipment failure in VH-JZU. 2 Misunderstanding of communications by the pilot of VH-JZU.