A 73-year-old man was pushed to the ground and robbed on Belleisle Street, Govanhill, at 18:45 on Wednesday.
An 83-year-old man is in hospital after three men barged into his flat in Garturk Street at 22:45 and robbed him.
The suspects in both are described as "of Eastern European appearance". It is not yet known if they are linked.
The 73-year-old man was pushed to the ground and robbed by a man was is described as of Eastern European appearance, dark skinned and in his late teens.
He was wearing a black leather jacket, grey hooded top and blue denims.
The victim did not require hospital treatment.
The victim in the second robbery sustained facial injuries and is currently in a stable condition in hospital.
The suspects in this case are described as of Eastern European appearance, in their early 20s. One of them had short shaved dark hair.
Ch Insp Graham McInarlin, of Police Scotland, said: "At this time we cannot confirm if the two incidents are linked, however, inquiries are ongoing.
"Thankfully, neither man was seriously injured. However, I fully recognise and understand the impact this has on the local community and in particular our elderly residents.
"The seriousness of these incidents is not lost on me and be re-assured that Police Scotland is treating these incidents head on and will fully commit all resources, both local and national to deal with those responsible."
Ch Insp McInarlin said "a significant additional number of officers" would be deployed to the area, including mounted police and a specially trained plain clothes unit and these would be maintained "indefinitely".
He added: "The men responsible for these robberies are nothing but cowards.
"They are despicable and deserve all that is coming to them and I am determined to catch them and put them behind bars."
Police are to significantly increase the number of officers in a racially diverse area of Glasgow after two elderly men were injured and robbed.