Gareth McAllister, 18, is also accused of inflicting wounds on a 74-year-old man during a triple stabbing in Glengormley, County Antrim.
All three alleged victims are members of the same family.
Mr McAllister, of Rogan Manor in Newtownabbey, was arrested at a nearby petrol station on Wednesday night.
A man aged 20 had suffered a slash wound to his forehead in an alleged attack at the house on the Antrim Road.
His 51-year-old father and his grandfather also sustained cuts as further violence broke out at the nearby garage, according to police.
Mr McAllister appeared before Belfast Magistrates' Court on a total of 10 counts.
He is charged with the attempted murders of Jonathan and John Green, and assault occasioning actual bodily harm to Derek Green.
The other alleged offences include: possessing a bread knife in public; four assaults on police representatives; a separate assault on John Green last Saturday; and criminal damage to his front door.
Mr McAllister spoke only to confirm he understood the charges against him.
Although no further details were disclosed, a detective constable said he could connect the accused to the alleged offences.
A defence lawyer said he was not applying for bail "at this time".
A judge remanded Mr McAllister in custody to appear again by video-link next Thursday.

The announcement came as the London venue unveiled its new programme which includes plays starring Ralph Fiennes, Andrew Garfield and Tamsin Greig.
NT boss Rufus Norris said Sunday performances would stop because they were "always the last performances to sell".
The last Sunday show will be Damon Albarn's musical Wonder.land in April.
Sunday performances in the Olivier and Lyttelton theatres began in 2008 and took place about 35 weeks a year.
Norris said the decision to stop them was taken after the theatre "looked very carefully at the evidence over the last few years".
Giving more detail, executive director Lisa Burger said: "The fact is that there aren't as many audiences coming to Sunday performances.
"Given the tight financial situation that we are in we decided that was one of the things we had to give up."
The NT building on the South Bank will, however, remain open to the public on Sundays over the summer.
Among the plays coming up at the National's Olivier theatre is Twelfth Night in February 2017 - with Tamsin Greig turning the traditionally male role of Malvolio into Malvolia.
"That play is about lots of gender confusion anyway," Norris said.
There will be more Shakespeare in early 2018 when Ralph Fiennes will star in Antony and Cleopatra. The role of Cleopatra is yet to be cast.
Other highlights include:
Norris described the blend of re-imagined popular classics, new plays and musical pieces as "hopefully a broad programme which will underline our commitment that we believe that theatre is for everyone".
A teenager has been remanded in custody charged with the attempted murder of a father and son in a knife attack on the outskirts of north Belfast.
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The National Theatre has decided to axe Sunday performances due to its "tight financial situation".