The relationship was nicknamed Morganders as well as Grody by fans.
At 73 Seconds, Greg was introduced to Morgan by Nick and Greg was slightly flirty towards Morgan but their conversation lead to an awkward pause after meeting Morgan , Greg was suprised that Morgan is Ecklie's daughter and Nick also warned Greg not to do what he was thinking because Morgan is Ecklie's daughter.Greg also mentioned to Sara that he just met Morgan.
At Tell-Tale Hearts, It was Morgan's first case and she is still adjusting living in Vegas. As her first task was to check for evidence of the surrounding areas as Greg was processing the inside of the crime scene. Greg also gives her the nickname Hollywood.
In Bittersweet was Morgan's and Greg's first case together alone and it was revealed that Morgan is not interested in dating a co-worker as Greg trying to look his best to impress Morgan and Greg was slightly jealous when Morgan was interested in handsome male model who is advertising chocolate.
In CSI Down Greg continued to be flirty with Morgan and he was extremely worried when a medavac helicopter which was Morgan onboard was hijacked and Greg was deeply concerned for Morgan's safety more than the rest of the team. Greg expressed his anger on the hijacker's daughter when she set her father up to trap and sent a gang after them. Even yelling "If they hurt her I swear to you!" while being held back and taken out of the room, but not before he kicks over a nearby chair.
In Crime After Crime When Greg got back from examining everyone at a party that the Host was murdered, D.B. tells him to go help Morgan on a case and meet her at a motel. He walks away with a smug smile on his face while D.B. calls back "It's a crime scene, not a date! Ya wacky kid." during which he still has a smile on his face.
In Stealing home D.B. Russell told Morgan to find the murder weapon and she can take "her boyfriend Greg" with her and leaving Morgan with a confused look on her face.
In CSI Unplugged They run into each other. When she explains that she is stressed because she cannot figure out what a white substance was and she said "Russell told me to use my head and my hands. I'm using my head, my hands, not so helpful" and he says "Maybe I have another idea for your hands." Her reaction prompts him to quickly explain himself. At the end of the episode, when she is about to put the old microscope back, he comes up to her and asks her if she's sure about that and that it might come in handy.
In Dune and Gloom Julie Finlay was talking to her boyfriend on the phone and walks in a observation room without knowing Morgan Brody was in the room leaving her with a suprised face and Finn hangs up the phone and leaving Finn embarrassed and explains the situation with Morgan but Morgan says " Don't be embarrassed I'm glad someone around here has a personal life' and Finn replies "Really Aren't you going out with Greg?" but Morgan quickly denies it. But later that episode while going around the scene Greg offers Morgan they should grab a beer and Morgan accepted the offer.
In It Was a Very Good Year, Greg is really upset about the death of a music historian, that he'd met in the past (actually, the victim was an old crush). Morgan said really beautiful things for him, for example, that he was a handsome guy and really nice (Putting her hands, on his). After, she said to him that he had to move forward, and that "The best is yet to come."
In Risky Business Class, Donna Hoppe says that Greg and Morgan are really cute together. She also said that "Hojem-Sanders" and "Ecklie" were both Norwegians names, so they had to be careful, because they could be "kissing cousins". They got really embarrassed.
Season 13 behind the scenes:
The writers of CSI has tweeted this behind the scene of Morgan and Greg. The emotional scene shows Morgan was covered in blood and Greg is comforting Morgan or possibly Morgan telling Greg what happened.
Both fans and the stars themselves seems to like the idea of Greg and Morgan being more than just friends.
Greg to Morgan: " You miss me already?" (CSI Down)
Greg: "You need professional help?"
Morgan:"Oh you offering your services?"
Greg: "Wouldn't it be safer for Morgan... and the others, if we just let him run?"
Greg: "If they hurt her I swear to you!"
Greg running towards Morgan: "Morgan! Are you hurt?"
Morgan: "You still owe me one"
D.B. to Greg: "It's a crime scene, not a date, ya wacky kid..." (Crime After Crime)
D.B. to Morgan: "You can take boyfriend Greg with you" (Stealing Home)
Morgan: "Russell told me to use my head and my hands. I'm using my head, my hands, not so helpful"
Greg: "Maybe I have another spot for your hands" (CSI Unplugged)
Morgan: "Why go old school..."
Greg: "When you can go ancient"