You will have to serve the appropriate notice to cease and then notice to quit before you can file an eviction action. As there are many potential pitfalls, you should consult an attorney involved in landlord/tenant actions because there are requirements and time frames for each notice.
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Unless your property is a small, owner-occupied building (3 units or less), you must identify a "cause" for terminating a lease as provided in NJ's Anti-Eviction Act, serve whatever notices are required for the applicable "cause" and then file a complaint for eviction in Essex County's Landlord-Tenant court. If your property is a small, owner-occupied building, then you don't need to identify a cause for terminating the tenancy, but still need to serve a Notice to Quit and if the tenant fails to move out by the date set forth in the notice, you still must file the eviction complaint with the court. Under the Anti-Eviction Act, at the end of a lease, if there is no new lease signed, the relationship automatically converts to a month-to-month tenancy.
Unless the proeprty is an owner occupied building with not more than two rental units you can only evict a tenant for cause under the Anti-Eviction Act. Residential tenants have virtually a life-time tenancy unless they violate the terms of the lease or there is other good cause under the Act. If there is cause, there are also notice provisions which must be strictly complied with before you can bring an action for possession in landlord-tenant court. I suggest you consult with an experienced landlord-tenant attorney before you take any action.