Illustrative operations involved in using multiple devices 10 (e.g., devices 10A and 10B) are shown in FIG. 17. During the operations of block 60, devices 10A and devices 10B may be operated in an independent operating mode (see, e.g., state 50-1 of FIG. 13). During this mode, device 10A and/or device 10B may use components 38 (e.g., sensors 32) to monitor for adjacency between devices 10A and 10B. If desired, output from components 38 in device 10A and/or device 10B may be used to initially detect that a sidewall along an edge of device 10B is adjacent to one of the sidewalls along an edge of device 10A and this initial detection may be confirmed using wireless communications between devices 10A and 10B (sometimes referred to as handshaking, authentication, or acknowledgement). For example, if device 10A detects the presence of a possible adjacent device, device 10A can issue a near-field communications request or other wireless request asking adjacent devices to identify themselves. In response, device 10B can use its sensor(s) 32 to confirm adjacency and can wirelessly provide device 10A with this information and/or information on the identity of device 10B and/or other information confirming that device 10B is authorized and desires to jointly operate with device 10A. Configurations in which devices 10A and/or 10B generate confirmatory patterns of magnetic fields (e.g., a magnetic field produced by device 10B that is detected by a magnetic sensor in device 10A), acoustic signals or vibrations (e.g., a sound or vibration that is generated by device 10B and detected by a microphone or accelerometer in device 10A), light (e.g., light from a light-emitting diode in device 10B that is detected by a light detector in device 10A), and/or other in which devices 10A and 10B otherwise generate unidirectional and/or bidirectional localized confirmatory information may also be used in determining adjacency. Simultaneous accelerometer signatures (e.g., simultaneous bumps that are detected by the accelerometers in each device when the devices first contact each other) may also be used as part of an adjacency detection scheme. In general, adjacency between devices 10A and 10B can be determined by using data from adjacency detection sensors, receipt of wireless communications from an adjacent device, and/or other operations that take place in one of devices 10A and 10B or that take place in both devices 10A and 10B. Configurations in which adjacency status information (e.g., sensor readings indicative of device adjacency) is shared between devices 10A and 10B (e.g., when adjacency is confirmed when device 10A detects the presence of device 10B with a sensor in device 10A and when device 10B detects the presence of device 10A with a sensor in device 10B) may enhance adjacency detection reliability. In response to determining that devices 10A and 10B are not adjacent (from information gathered using one or more of sensors 32 and/or other detection mechanisms), monitoring may continue at block 60, as indicated by line 62.