i think, you just forgot the second pair of curly brackets({}):

{\externalfigure[Ex6a]}{}
{\externalfigure[Ex6b]}{}

for me (mac, context 2009.04.10 18:02 MKII) your code works fine like  
this, the two side by side.

Greets



On May 9, 2009, at 10:19 , Robert Blackstone wrote:

>
>
> On Fri, May 8, 2009 at 10:23 PM, <ntg-context-request@ntg.nl>, Mojca  
> Miklavec and Thomas Floeren wrote, respectively:
>
>
> On Fri, May 8, 2009 at 21:53, Robert Blackstone wrote:
> > Hi All,
> > I am working on a text that contains many combined figures, some  
> side by
> > side, ?some arranged vertically. I use, following ?ConTeXt, an  
> excursion?,
> > \startcombination[1*2] and \startcombination[2*1] respectively.  
> The first
> > one works, the second doesn?t, that is, it also places the figures  
> one above
> > the other. It happens both with the ?MacTeX?-version of ConTeXt  
> and with the
> > minimals.
> > What can I do to place two figures side by side with a single  
> caption?
>
> Both variants work for me.
>
> \starttext
> \placefigure{some title}
> {\startcombination[1*2]
>        {\framed[width=5cm]{}}{}
>        {\framed[width=5cm]{}}{}
> \stopcombination}
> \placefigure{some title}
> {\startcombination[2*1]
>        {\framed[width=5cm]{}}{}
>        {\framed[width=5cm]{}}{}
> \stopcombination}
> \stoptext
>
> Mojca
>
>
> ------------------------------
>
>
> For me normally \startcombination[2*1] .. works. MKII; Side by side
> with a single caption.
> Please tell me if I didnt understand your problem.
>
> Greetings
> Tom
>
> Thanks to Mojca and Tom,
> With Mojca’s commands, {\framed[width=5cm]{}}{}, it works for me  
> too. But I do not want the figures framed. When I replace that piece  
> with {\externalfigure[NameofFigure]}, the figures are placed  
> vertically, both with [2*1] and with [1*2].
> I have uploaded a folder with a small testfile, which on my Mac  
> shows this behaviour, as you can see in the pdf. (For convenience I  
> have entered the two possibilities in the testfile, one of them  
> commented out.) It can be downloaded from http://web.me.com/blackstone.robert/filechute/Combining_Figures.zip 
> .
> Maybe there are some other errors in the file that I do not know of.
> Thanks for the attention.
> Best regards,
> Robert Blackstone
>
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