Two Navigation Drawer on same Activity

You can use drawer layout

 <android.support.v4.widget.DrawerLayout
   xmlns:android="http://schemas.android.com/apk/res/android"
   android:id="@+id/drawer_layout"
   android:layout_width="match_parent"
   android:layout_height="match_parent">
   <!-- The main content view -->

   <FrameLayout
      android:id="@+id/content_frame"
    android:layout_width="match_parent"
    android:layout_height="match_parent" />

<!-- The navigation drawer -->
    <ListView android:id="@+id/left_drawer"
       android:layout_width="240dp"
       android:layout_height="match_parent"
       android:layout_gravity="start"
       android:choiceMode="singleChoice"
       android:divider="@android:color/transparent"
       android:dividerHeight="0dp"
       android:background="#111"/>


   <ListView android:id="@+id/right_drawer"
       android:layout_width="240dp"
       android:layout_height="match_parent"
       android:layout_gravity="end"
       android:choiceMode="singleChoice"
       android:divider="@android:color/transparent"
       android:dividerHeight="0dp"
       android:background="#111"/>
 </android.support.v4.widget.DrawerLayout>

ALso check the documantation https://developer.android.com/training/implementing-navigation/nav-drawer.html

Make sure you are using toolbar not action bar

Yes you can add two ListView inside your drawer layout, one listview should have gravity start and other have end.